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Encyclopedia > Cosmic inflation
Physical Cosmology
Physical Cosmology

Universe · Big Bang
Age of the universe
Timeline of the Big Bang...
Ultimate fate of the Universe Image File history File links Download high resolution version (2198x1274, 1278 KB)WMAP map of CMB anisotropy, from NASA.gov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Physical cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... The age of the universe, according to the Big Bang theory, is the time elapsed between the Big Bang and the present day. ... A graphical timeline is available here: Graphical timeline of the Big Bang This timeline of the Big Bang describes the events that have occurred and will occur according to the scientific theory of the Big Bang, using the cosmological time parameter of comoving coordinates. ... The ultimate fate of the universe is a topic in physical cosmology. ...

Early universe

Inflation · Nucleosynthesis
Cosmic gravitational waves
Cosmic microwave background In cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than H-1, the normal, light hydrogen, during the early phases of the universe, shortly after the Big Bang. ... This article or section is in need of attention from an expert on the subject. ... In cosmology, the cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR, also referred as relic radiation) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe. ...

Expanding universe

Redshift · Hubble's law
Metric expansion of space
Friedmann equations · FLRW metric Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... Hubbles law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... // The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations of general relativity and which describes a homogeneous, isotropic expanding/contracting universe. ...

Structure formation

Shape of the universe
Structure formation
Galaxy formation
Large-scale structure
The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ... It has been suggested that this article or section be merged into Large-scale structure of the cosmos. ... In astrophysics, the questions of galaxy formation and evolution are: How, from a homogeneous universe, did we obtain the very heterogeneous one we live in? How did galaxies form? How do galaxies change over time? A spectacular head-on collision between two galaxies is seen in this NASA Hubble Space... Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ...

Components

Lambda-CDM model
Dark energy · Dark matter A pie chart indicating the proportional composition of different energy-density components of the universe. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ... In astrophysics and cosmology, dark matter refers to hypothetical matter of unknown composition that does not emit or reflect enough electromagnetic radiation to be observed directly, but whose presence can be inferred from gravitational effects on visible matter. ...

History

Timeline of cosmology... This lists a timeline of cosmological theories and discoveries. ...

Cosmology experiments

Observational cosmology
2dF · SDSS
CoBE · BOOMERanG · WMAP Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. ... In astronomy, the 2dF Galaxy Redshift Survey (Two-degree-Field Galaxy Redshift Gurvey), or 2dFGRS is a redshift survey conducted by the Anglo-Australian Observatory in the 1990s. ... SDSS Logo The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2. ... The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was the first satellite built dedicated to cosmology. ... The Telescope being readied for launch The BOOMERanG experiment (Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics) measured the cosmic microwave background radiation of a part of the sky during three sub-orbital (high altitude) balloon flights. ... Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ...

Scientists

Einstein · Friedman · Lemaître
Hubble · Penzias · Wilson
Gamow · Dicke · Zel'dovich
Mather · Smoot · others Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is best known for his theory of relativity and specifically mass-energy equivalence, . He was awarded the 1921 Nobel Prize in Physics for his services to Theoretical Physics, and especially for his discovery of the... Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман) (June 16, 1888 – September 16, 1925) was a Russian cosmologist and mathematician. ... Father Georges-Henri Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer. ... Edwin Powell Hubble (November 29, 1889 – September 28, 1953) was an American astronomer. ... Arno Allan Penzias (born April 26, 1933) is an American physicist and winner of the 1978 Nobel Prize in physics. ... Robert Woodrow Wilson Robert Woodrow Wilson (born January 10, 1936) is an American physicist. ... George Gamow (pronounced GAM-off) (March 4, 1904 – August 19, 1968) , born Georgiy Antonovich Gamov (Георгий Антонович Гамов) was a Ukrainian born physicist and cosmologist. ... Robert Henry Dicke (May 6, 1916 – March 4, 1997) was an American experimental physicist, who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity. ... Yakov Borisovich Zeldovich (Russian:Яков Борисович Зельдович) (March 8, 1914 – December 2, 1987) was a prolific Soviet physicist. ... John Cromwell Mather (b. ... George Fitzgerald Smoot III (born February 20, 1945) is an American astrophysicist and cosmologist awarded the 2006 Nobel Prize in Physics with John C. Mather for their discovery of the black body form and anisotropy of the cosmic microwave background radiation. This work helped cement the big-bang theory of... This is a partial list of persons who have made major contributions to the development of standard mainstream Cosmology. ...

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In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density.[1] As a direct consequence of this expansion, all of the observable universe originated in a small causally-connected region. Inflation answers the classic conundrums of the big bang cosmology: why does the universe appear flat, homogeneous and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the big bang, a highly curved, inhomogeneous universe. Inflation also explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the universe (see galaxy formation and evolution and structure formation). Physical cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... Negative pressure is misunderstood as pressure less than that of the ambient atmosphere. ... Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). ... Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ... Look up Homogeneous in Wiktionary, the free dictionary. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ... Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ... In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, arising from Werner Heisenbergs uncertainty principle. ... In astrophysics, the questions of galaxy formation and evolution are: How, from a homogeneous universe, did we obtain the very heterogeneous one we live in? How did galaxies form? How do galaxies change over time? A spectacular head-on collision between two galaxies is seen in this NASA Hubble Space... It has been suggested that this article or section be merged into Large-scale structure of the cosmos. ...


Inflation was first proposed by American physicist and cosmologist Alan Guth in 1981[2] and was given its modern form independently by Andrei Linde,[3] and by Andreas Albrecht and Paul Steinhardt.[4] Alan Harvey Guth (born February 27, 1947) is a physicist and cosmologist. ... Andrei Linde is an American physicist and professor of Physics at Californias Stanford University. ... Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. ...


While the detailed particle physics mechanism responsible for inflation is not known, the basic picture makes a number of predictions that have been confirmed by observational tests. Inflation is thus now considered part of the standard hot big bang cosmology. The hypothetical particle or field thought to be responsible for inflation is called the inflaton. Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... The magnitude of an electric field surrounding two equally charged (repelling) particles. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ...

Contents

Overview

Inflation suggests that there was a period of exponential expansion in the very early universe. The expansion is exponential because the distance between any two fixed observers is increasing exponentially, due to the metric expansion of space (a spacetime with this property is called a de Sitter space). The physical conditions from one moment to the next are stable: the rate of expansion, called the Hubble parameter, is nearly constant, which leads to high levels of symmetry. Inflation is often called a period of accelerated expansion because the distance between two fixed observers is increasing at an accelerating rate as they move apart. (However, this does not mean that the Hubble parameter is increasing, see deceleration parameter.) The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... In mathematics and physics, n-dimensional de Sitter space, denoted , is the maximally symmetric, simply-connected, Lorentzian manifold with constant positive curvature. ... Hubbles law is the statement in astronomy that the redshift in light coming from distant galaxies is proportional to their distance. ... The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of the universe. ...


Cosmic inflation has the important effect of smoothing out inhomogeneities, anisotropies and the curvature of space. This pushes the universe into a very simple state, in which it is completely dominated by the inflaton field and the only significant inhomogeneities are the tiny quantum fluctuations in the inflaton. Inflation also dilutes exotic heavy particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the universe was only hot enough to form such particles before a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the observable universe. Together, these effects are called the inflationary "no-hair theorem"[5] by analogy with the no hair theorem for black holes. In physics, homogeneity is the quality of having all properties independent of the position. ... Look up anisotropy in Wiktionary, the free dictionary. ... The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... In astrophysics, the no-hair theorem states that black holes are completely characterized only by three externally observable parameters: mass, electrical charge, and angular momentum. ... Simulated view of a black hole in front of the Milky Way A black hole is an object with a gravitational field so powerful that a region of space becomes cut off from the rest of the universe – no matter or radiation (including light) that has entered the region can...


The "no-hair" theorem works essentially because the universe expands by an enormous factor during inflation. In an expanding universe, energy densities generally fall as the volume of the universe increases. For example, the density of ordinary "cold" matter (dust) goes as the inverse of the volume: when linear dimensions double, the energy density goes down by a factor of eight. The energy density in radiation goes down even more rapidly as the universe expands: when linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen. During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in inhomogeneities, curvature, anisotropies and exotic particles is falling, and through sufficient inflation these become negligible. This leaves an empty, flat, and symmetric universe, which is filled with radiation when inflation ends. Energy density is the amount of energy stored in a given system or region of space per unit volume or per unit mass, depending on the context. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ...


A key requirement is that inflation must continue long enough to produce the present observable universe from a single, small inflationary Hubble volume. This is necessary to ensure that the universe appears flat, homogeneous and isotropic at the largest observable scales. This requirement is generally thought to be satisfied if the universe expanded by a factor of at least 1026 during inflation.[6] At the end of inflation, a process called reheating occurs, in which the inflaton particles decay into the radiation that starts the hot big bang. It is not known how long inflation lasted but it is usually thought to be extremely short compared to the age of the universe. Assuming that the energy scale of inflation is between 1015 and 1016 GeV, as is suggested by the simplest models, the period of inflation responsible for the observable universe probably lasted roughly 10-33 seconds.[7] A Hubble volume refers to a volume of space, usually defined as a cube where each axis is approximately 13. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. ... A GEV (or Ground Effect Vehicle) is vehicle that takes advantage of the aerodynamic principle of ground effect (or Wing-in-ground). ...


Motivation

Inflation resolves several problems in the Big Bang cosmology that were pointed out in the 1970s.[8] These problems arise from the observation that to look like it does today, the universe would have to have started from very finely tuned, or "special" initial conditions near the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the universe to this special state, thus making a universe like ours much more natural in the context of the Big Bang theory. According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ...


Horizon problem

Main article: horizon problem

The horizon problem[9][10][11] is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with the cosmological principle. The gas molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only the matter and radiation known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than speed of light - thus have never come in to causal contact: in the history of the universe, back to the earliest times, it has not been possible to send a light signal between the two regions. Because they have no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). This is because the Hubble radius in a radiation- or matter-dominated universe expands much more quickly than physical lengths and so points that are out of communication are coming into communication. Historically, two proposed solutions were the Phoenix universe of Georges Lemaître[12] and the related oscillatory universe of Richard Chase Tolman,[13] and the Mixmaster universe of Charles Misner.[10][14] Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of entropy over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the universe more chaotic, could lead to statistical homogeneity and isotropy. When we look at the CMB it comes from 15 billion light years away. ... When we look at the CMB it comes from 15 billion light years away. ... The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ... This article or section does not cite any references or sources. ... Radiation as used in physics, is energy in the form of waves or moving subatomic particles. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... Although causality, the relationship between causes and effects, is often examined in the fields of philosophy, computer science, and statistics, it has a place in the study of physics as well. ... See universe for a general discussion of the universe. ... Father Georges-Henri Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer. ... The oscillatory universe is the hypothesis, attributable to Richard Tolman, that the universe undergoes an infinite series of oscillations, each beginning with a big bang and ending with a big crunch. ... This article lacks information on the importance of the subject matter. ... The Mixmaster Universe is a solution to Einsteins general relativity studied by Charles Misner in an effort to better understand the dynamics of the early universe [1]. He hoped to solve the horizon problem in a natural way by showing that the early universe underwent an oscillatory, chaotic epoch. ... Charles W. Misner is one of the authors of Gravitation. Kip Thorne John Archibald Wheeler http://www. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ...


Flatness problem

Main article: Flatness problem

Another problem is the flatness problem (which is sometimes called one of the Dicke coincidences, with the other being the cosmological constant problem).[15][16] It had been known in the 1960s[citation needed] that the density of matter in the universe was comparable to the critical density necessary for a flat universe (that is, a universe whose large scale geometry is the usual Euclidean geometry, rather than a non-Euclidean hyperbolic or spherical geometry). Therefore, regardless of the shape of the universe the contribution of spatial curvature to the expansion of the universe could not be much greater than the contribution of matter. But as the universe expands, the curvature redshifts away more slowly than matter and radiation. Extrapolated into the past, this presents a fine-tuning problem because the contribution of curvature to the universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at big bang nucleosynthesis, for example). This problem is exacerbated by recent observations of the cosmic microwave background that have demonstrated that the universe is flat to the accuracy of a few percent. The flatness problem is a cosmological problem with the Big Bang theory, which is solved by hypothesising an inflationary universe. ... The flatness problem is a cosmological problem with the Big Bang theory, which is solved by hypothesising an inflationary universe. ... Robert Henry Dicke (May 6, 1916 – March 4, 1997) was an American experimental physicist, who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as part of his theory of general relativity to achieve a stationary universe. ... In cosmology, the Big Crunch is a hypothesis that states the universe will stop expanding and start to collapse upon itself; a counterpart to the Big Bang. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. ... Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry describes hyperbolic, elliptic and absolute geometry, which are contrasted with Euclidean geometry. ... Lines through a given point P and hyperparallel to line l. ... Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... Fine Tuning is the name of XM Satellite Radios eclectic music channel. ... In cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than H-1, the normal, light hydrogen, during the early phases of the universe, shortly after the Big Bang. ...


Magnetic monopole problem

The magnetic monopole problem (sometimes called the exotic relics problem) is a problem that suggests that if the early universe were very hot, a large number of very heavy, stable magnetic monopoles would be produced. This was a problem with Grand Unified Theories, popular in the 1970s and 1980s, which proposed that at high temperatures (such as in the early universe) the electromagnetic force, strong and weak nuclear forces are not actually fundamental forces but arise due to spontaneous symmetry breaking from a much simpler gauge theory.[17] These theories predict a number of heavy, stable particles which have not yet been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "knot" in the magnetic field.[18][19] Monopoles are expected to be copiously produced in Grand Unified Theories at high temperature, and they should have persisted to the present day.[20][21] To very high precision, magnetic monopoles have been shown not to exist in nature[22], whereas according to the big bang theory (without cosmic inflation) they should have been copiously produced in the hot, dense early universe and since become the primary constituent of the universe. In physics, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle... Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ... 1970 (MCMLXX) was a common year starting on Thursday. ... 1980 (MCMLXXX) was a leap year starting on Tuesday. ... In physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... A Feynman diagram of a strong proton-neutron interaction mediated by a neutral pion. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ...


History

Inflation was proposed in 1981 by Alan Guth as a mechanism for resolving these problems.[2] There were several precursors, most importantly the work of Willem de Sitter which demonstrated the existence of a highly symmetric inflating universe, called de Sitter space. De Sitter, however, didn't apply it to any of the cosmological problems that interested Guth.[23] Contemporary with Guth, Alexei Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the universe with an exponentially expanding state.[24] Demosthenes Kazanas anticipated part of Guth's work by suggesting that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem,[25] and Sato suggesting that an exponential expansion could eliminate domain walls (another kind of exotic relic).[26] However, Guth was the first to assemble a complete picture of how all these initial conditions problems could be solved by an exponentially expanding state. Alan Harvey Guth (born February 27, 1947) is a physicist and cosmologist. ... Willem de Sitter (May 6, 1872 – November 20, 1934) was a mathematician, physicist and astronomer. ... In mathematics and physics, n-dimensional de Sitter space, denoted , is the maximally symmetric, simply-connected, Lorentzian manifold with constant positive curvature. ... It has been suggested that this article or section be merged into Observable universe. ... A domain wall is a theoretical 2-dimensional singularity. ...

The physical size of the Hubble radius (solid line) as a function of the linear expansion (scale factor) of the universe. During cosmic inflation, the Hubble radius is constant. The physical wavelength of a perturbation mode (dashed line) is also shown. The plot illustrates how the perturbation mode grows larger than the horizon during cosmic inflation before coming back inside the horizon, which grows rapidly during radiation domination. If cosmic inflation never happened, and radiation domination continued back until a gravitational singularity, then the mode would never been inside the horizon in the very early universe, at no causal mechanism could have ensured that the universe was homogeneous on the scale of the perturbation mode.
The physical size of the Hubble radius (solid line) as a function of the linear expansion (scale factor) of the universe. During cosmic inflation, the Hubble radius is constant. The physical wavelength of a perturbation mode (dashed line) is also shown. The plot illustrates how the perturbation mode grows larger than the horizon during cosmic inflation before coming back inside the horizon, which grows rapidly during radiation domination. If cosmic inflation never happened, and radiation domination continued back until a gravitational singularity, then the mode would never been inside the horizon in the very early universe, at no causal mechanism could have ensured that the universe was homogeneous on the scale of the perturbation mode.

Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a metastable state (it was supercooled) which it could only decay out of through the process of bubble nucleation via quantum tunneling. Bubbles of true vacuum spontaneously form in the sea of false vacuum and rapidly begin expanding at the speed of light. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. (Even though the bubbles are expanding at the speed of light, the bubbles are far enough apart that the expansion of space is causing the distance between them to expand much faster.) Image File history File links Inflationary_horizon_plot. ... Image File history File links Inflationary_horizon_plot. ... A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. ... Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ... A false vacuum is a metastable sector of a quantum field theory which appears to be a perturbative vacuum but is unstable to instanton effects which tunnel to a lower energy state. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ... A metastable system with a weakly stable state (1), an unstable transition state (2) and a strongly stable state (3) Metastability is the ability of a non-equilibrium state to persist for some period of time. ... Supercooling is the process of chilling a liquid below its freezing point, without it becoming solid. ... Bubbles in a soft drink each nucleate independently, responding to a decrease in pressure. ... Quantum tunneling is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ... In quantum field theory, the vacuum state, usually denoted , is the element of the Hilbert space with the lowest possible energy, and therefore containing no physical particles. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ...


This problem was solved by Andrei Linde[3] and independently by Andreas Albrecht and Paul Steinhardt[4] in a model named new inflation or slow-roll inflation (Guth's model then became known as old inflation). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a scalar field rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur. Andrei Linde is an American physicist and professor of Physics at Californias Stanford University. ... Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. ... In mathematics and physics, a scalar field associates a scalar to every point in space. ...


Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that tiny quantum fluctuations in the inflaton are created. These tiny fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in the Soviet Union in analyzing Starobinsky's similar model.[27][28][29] In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University.[30] The fluctuations were calculated by four groups working separately over the course of the workshop: Stephen Hawking;[31] Starobinsky;[32] Guth and So-Young Pi;[33] and James M. Bardeen, Paul Steinhardt and Michael Turner.[34] The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... The University of Cambridge (often Cambridge University), located in Cambridge, England, is the second-oldest university in the English-speaking world and has a reputation as one of the worlds most prestigious universities. ... Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ... James M. Bardeen is an American physicist, well known for his work in general relativity, particularly his role in formulating the laws of black hole mechanics. ... Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. ... Turner (not pictured) is employed by the University of Chicago Michael S. Turner is a cosmologist who coined the term dark energy. ...


Observational status

Inflation is a concrete mechanism for realizing the cosmological principle which is the basis of our model of physical cosmology: it accounts for the homogeneity, isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite.[35] This analysis shows that the universe is flat to an accuracy of at least a few percent, and that it is homogeneous and isotropic to a part in 10,000. The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ... WMAP image of the CMB anisotropy,Cosmic microwave background radiation(June 2003) The cosmic microwave background radiation (CMB) is a form of electromagnetic radiation that fills the whole of the universe. ... Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ...


In addition, inflation predicts that the structures visible in the universe today formed through the gravitational collapse of perturbations which were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations called a nearly-scale-invariant Gaussian random field (or Harrison-Zel'dovich spectrum) is very specific and has only two free parameters, the amplitude of the spectrum and the spectral index which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe).[36] Inflation predicts that the observed perturbations should be in thermal equilibrium with each other (these are called adiabatic or isentropic perturbations). This structure for the perturbations has been confirmed by the WMAP satellite and other cosmic microwave background experiments,[35] and galaxy surveys, especially the ongoing Sloan Digital Sky Survey.[37] These experiments have shown that the one part in 10,000 inhomogeneities observed have exactly the form predicted by theory. Moreover, the slight deviation from scale invariance has been measured. The spectral index, ns is equal to one for a scale-invariant spectrum. The simplest models of inflation predict that this quantity is between 0.92 and 0.98.[38][39][40][41] The WMAP satellite has measured ns = 0.95 and shown that it is different from one at the level of two standard deviations (2σ). This is considered an important confirmation of the theory of inflation.[35] This article or section does not cite its references or sources. ... In physics, scale invariance is the feature of physical objects of laws that do not change if the space is magnified, i. ... A Gaussian random field is random field involving Gaussian probability density functions of the variables. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ... A galaxy survey is a survey of galaxies in two or three dimensions. ... SDSS Logo The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ...


A number of theories of inflation have been proposed that make radically different predictions, but they generally have much more fine tuning than is necessary.[38][39] As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics. Fine Tuning is the name of XM Satellite Radios eclectic music channel. ...


Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature.[42] However, the third-year data revealed that the effect was a statistical anomaly.[35] Another effect has been remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer: the amplitude of the quadrupole moment of the cosmic microwave background is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to other new physics, foreground contamination, or even publication bias.[43] The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was the first satellite built dedicated to cosmology. ... Quadrupole magnet(four-pole), focus particle beams in a particle accelerator. ... The plane of the Ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... Publication bias, also called the positive outcome bias, is typically the tendency for researchers to publish experimental results that have a positive result (found something), while consequently not publishing findings which have a negative result (found that something did not happen). ...


An experimental program is underway to further test inflation with more precise measurements of the cosmic microwave background. In particular, high precision measurements of the so-called "B-modes" of the polarization of the background radiation will be evidence of the gravitational radiation produced by inflation, and they will also show whether the energy scale of inflation predicted by the simplest models (1015–1016 GeV) is correct.[39][40] These measurements are expected to be performed by the Planck satellite, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere with these measurements.[44] Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars turned on), may measure the power spectrum with even greater resolution than the cosmic microwave background and galaxy surveys, although it is not known if these measurements will be possible or if interference with radio sources on earth and in the galaxy will be too great.[45] In cosmology, the cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR, also referred as relic radiation) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... A GEV (or Ground Effect Vehicle) is vehicle that takes advantage of the aerodynamic principle of ground effect (or Wing-in-ground). ... Planck is a European Space Agency satellite to be launched in 2007. ... 21 centimeter radiation is radiation produced during a hyperfine transition of neutral hydrogen from the triplet to the singlet state. ... Stars can be grouped into two general types called Population I and Population II. The criteria for classification include space velocity, location in the galaxy, age, chemical composition, and differences in distribution on the Hertzsprung-Russell diagram. ... It has been suggested that this article or section be merged with Radio waves. ...


As of 2006, it is unclear what relationship if any the period of cosmic inflation has to do with dark energy.[citation needed] Dark energy is broadly similar to inflation, and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, 10-12 GeV, roughly 27 orders of magnitude less than the scale of inflation. In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ...


Theoretical status

Unsolved problems in physics: Is the theory of cosmic inflation correct, and if so, what are the details of this epoch? What is the hypothetical inflaton field giving rise to inflation?

In the early proposal of Guth, it was thought that the inflaton was the Higgs field, the field which explains the mass of the elementary particles.[2] It is now known that the inflaton cannot be the Higgs field. Other models of inflation relied on the properties of grand unified theories.[4] Since the simplest models of grand unification have failed, it is now thought by many physicists that inflation will be included in a supersymmetric theory like string theory or a supersymmetric grand unified theory. A promising suggestion is brane inflation. At present, however, inflation is understood principally by its detailed predictions of the initial conditions for the hot early universe, and the particle physics is largely ad hoc modelling. As such, despite the stringent observational tests inflation has passed, there are many open questions about the theory. Image File history File links No higher resolution available. ... This is a list of some of the unsolved problems in physics. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... Higgs bosons are hypothetical elementary particles predicted to exist by the Standard Model of particle physics. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ... In particle physics, supersymmetry is a hypothetical symmetry that relates bosons and fermions. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ...


Fine-tuning problem

One of the most severe challenges for inflation arises from the need for fine tuning in inflationary theories. In new inflation, the slow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.[46] In order for the new inflation theory of Linde, Albrecht and Steinhardt to be successful, therefore, it seemed that the universe must have a scalar field with an especially flat potential and special initial conditions. In theoretical physics, fine-tuning is a necessary procedure of fudging and very accurate adjusting of the values of the parameters of a theory in order for various physical quantities to be very small. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... It has been suggested that this article or section be merged with Potential. ... Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ...


Andrei Linde proposed a theory known as chaotic inflation in which he suggested that the conditions for inflation are actually satisfied quite generically and inflation will occur in virtually any universe that begins in a chaotic, high energy state and has a scalar field with unbounded potential energy.[47] However, in his model the inflaton field necessarily takes values larger than one Planck unit: for this reason, these are often called large field models and the competing new inflation models are called small field models. In this situation, the predictions of effective field theory are thought to be invalid, and renormalization should cause large corrections that could prevent inflation.[48] This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models of inflation.[49] While inflation depends on quantum field theory (and the semiclassical approximation to quantum gravity) in an important way, it has not been completely reconciled with these theories. The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). ... Figure 1. ... Semiclassical gravity is the approximation to the theory of quantum gravity in which one treats matter fields as being quantum and the gravitational field as being classical. ... This article or section does not adequately cite its references or sources. ...


Robert Brandenberger has commented on fine-tuning in another situation.[50] The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. There are strong suggestions that this scale is around 1016 GeV or 10−3 times the Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a hierarchy problem): the energy density given by the scalar potential is down by 10−12 compared to the Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification. A GEV (or Ground Effect Vehicle) is vehicle that takes advantage of the aerodynamic principle of ground effect (or Wing-in-ground). ... The Planck energy is the natural unit of energy, denoted by EP. 1. ... In theoretical physics, a hierarchy problem occurs when the fundamental parameters (couplings or masses) of some Lagrangian are vastly different (usually larger) than the parameters measured by experiment. ... The Planck density is the natural unit of density, denoted by ρP. ρP = Planck mass / (Planck length)3 = ≈ 5. ...


Eternal inflation

Cosmic inflation seems to be eternal the way it is theorised. Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes bring it back up to previous levels. These regions in which the inflaton fluctuates upwards expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. This steady state, which first developed by Vilenkin,[51] is called "eternal inflation". It has been shown that any inflationary theory with an unbounded potential is eternal.[52] It is a popular belief among physicists that this steady state cannot continue forever into the past.[53][54][55] The inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space will collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the universe's initial conditions. This interpretation is disputed by Linde, however.[56] The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... In mathematics and physics, n-dimensional de Sitter space, denoted , is the maximally symmetric, simply-connected, Lorentzian manifold with constant positive curvature. ... A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. ...


Initial conditions

Some physicists have tried to avoid this problem by proposing models for an eternally inflating universe with no origin.[57][58][59][60] These models propose a special "initial" hypersurface when the universe has some minimum size and from which time begins.


Other proposals attempt to describe the ex nihilo creation of the universe quantum cosmology and the following inflation. Vilenkin put forth one such scenario.[51] Hartle and Hawking proposed the no-boundary proposal for the initial creation of the universe in which inflation comes about naturally.[61] In theoretical physics, quantum cosmology is a young field attempting to study the effect of quantum mechanics on the earliest moments of the universe after the Big Bang. ... In theoretical physics, the Hartle-Hawking state, named after James Hartle and Stephen Hawking, is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the Universe. ...


Alan Guth has described the inflationary universe as the "ultimate free lunch":[62] new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) both the first law of thermodynamics or energy conservation and the second law of thermodynamics or the arrow of time problem. However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the universe came about by a quantum fluctuation. Donald Page was an outspoken critic of inflation because of this anomaly. [63] He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory further aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase. The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ... For the physical concepts, see conservation of energy and energy efficiency. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ... This article or section does not cite its references or sources. ... This article or section does not cite its references or sources. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ...


Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle-Hawking initial state.[64] Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the universe.[citation needed] Recently, Lisa Dyson, Matthew Kleban and Leonard Susskind argued using the holographic principle that spontaneous inflation is exceedingly improbable.[65] Albrecht and Lorenzo Sorbo have argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state, compared with a non-inflationary cosmos overwhelmingly favours the inflationary scenario, simply because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than any required for a non-inflationary alternative, which outweighs any entropic considerations.[66] Leonard Susskind is the Felix Bloch professor of theoretical physics at Stanford University in the field of string theory and quantum field theory. ... The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory that lives in the boundary of that region. ...


Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects.[67] Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations which have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. There has been some disagreement about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.[citation needed]


Reheating

The end of inflation is called reheating or thermalization because the large potential energy decays into particles and fills the universe with radiation. Because the nature of the inflaton is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance.[68][69] The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...


Non-eternal inflation

Another kind of inflation, called hybrid inflation, is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state.[70] Unlike most other models of inflation, many versions of hybrid inflation are not eternal. [71] [72]


In hybrid inflation, one of the scalar fields is responsible for most of the energy density (thus determining the rate of expansion), while the other is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches at the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the this inflaton down its potential, leading to termination of inflation.


Inflation and string cosmology

The discovery of flux compactifications have opened the way for reconciling inflation and string theory.[73] A new theory, called brane inflation suggests that inflation arises from a D-brane falling into a deep Klebanov-Strassler throat. This theory, governed by the Dirac-Born-Infeld action, is very different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism. In physics, compactification plays an important part in string theory. ... In theoretical physics, D-branes are a special class of p-branes, named for the mathematician Johann Dirichlet. ... In theoretical physics, a cascading gauge theory is a gauge theory whose coupling rapidly changes with the scale in such a way that Seiberg duality must be applied many times. ... The string landscape is an idea to implement the anthropic principle, in particular Steven Weinbergs proposal for anthropic selection of the vacuum density, in string theory. ...


Alternatives to inflation

String theory requires that, in addition to the three spatial dimensions we observe, there exist additional dimensions that are curled up or compactified (see also Kaluza-Klein theory). Extra dimensions appear as a frequent component of supergravity models and other approaches to quantum gravity. This begs the question: why did four space-time dimensions become large, and the rest become unobservably small? An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa[74]. This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of spacetime can only expand if the strings that wind around it can efficiently annihilate each other. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will generically intersect (and, presumably, annihilate) is three. Therefore, one argues that the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. For a recent review, see [75]. Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... In physics, compactification plays an important part in string theory. ... In physics, Kaluza-Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. ... In theoretical physics, supergravity (supergravity theory) refers to a field theory which combines the two theories of supersymmetry and general relativity. ... This article or section does not adequately cite its references or sources. ... Cumrun Vafa is a leading string theorist from Harvard University where he started as a Harvard Junior Fellow. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... Transversality in mathematics is a notion that describes how spaces can intersect; transversality can be seen as the opposite of tangency, and plays a role in general position. ...


The ekpyrotic and cyclic models are also considered competitors to inflation. These models solve the horizon problem through an expanding epoch well before the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch. The universe passes through the Big Crunch and emerges in a hot Big Bang phase. In this sense they are reminiscent of the oscillatory universe proposed by Richard Chace Tolman: however in Tolman's model the total age of the universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. The ekpyrotic universe or ekpyrotic scenario is a cosmological theory of the origin of the universe. ... The cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. ... When we look at the CMB it comes from 15 billion light years away. ... In physical cosmology, the Big Crunch is the hypothesis that the universe will collapse upon itself after its expansion eventually stops — a counterpart to the Big Bang. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... The oscillatory universe is the hypothesis, attributable to Richard Tolman, that the universe undergoes an infinite series of oscillations, each beginning with a big bang and ending with a big crunch. ... ...

See also: Brane cosmology

Brane cosmology is a protoscience motivated by, but not rigorously derived from, superstring theory and M-theory. ...

Notes

  1. ^ Liddle and Lyth (2000) and Mukhanov (2005) are recent cosmology textbooks with extensive discussions of inflation. Kolb and Turner (1988) and Linde (1990) miss some recent developments, but are still widely used. Peebles (1993) provides a technical discussion with historical context. Recent review articles are Lyth and Riotto (1999) and Linde (2005). Guth (1997) and Hawking (1998) give popular introductions to inflation with historical remarks.
  2. ^ a b c A. H. Guth, "The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems", Phys. Rev. D 23, 347 (1981).
  3. ^ a b A. Linde, "A New Inflationary Universe Scenario: A Possible Solution Of The Horizon, Flatness, Homogeneity, Isotropy And Primordial Monopole Problems", Phys. Lett. B 108, 389 (1982).
  4. ^ a b c A. Albrecht and P. J. Steinhardt, "Cosmology For Grand Unified Theories With Radiatively Induced Symmetry Breaking," Phys. Rev. Lett. 48, 1220 (1982).
  5. ^ Kolb and Turner (1988).
  6. ^ This is usually quoted as 60 e-folds of expansion, where e60 ≈ 1026. It is equal to the amount of expansion since reheating, which is roughly Einflation/T0, where T0 = 2.7 K is the temperature of the cosmic microwave background today. See, e.g. Kolb and Turner (1998) or Liddle and Lyth (2000).
  7. ^ This comes from the Friedmann equation, which, written in terms of the Hubble time is 3t − 2 = 8πG(1015GeV)4, where G is Newton's constant. Inflation is expected to last at least 60 Hubble times. This is a lower bound, however. The overall epoch of inflation could have been somewhat longer.
  8. ^ Much of the historical context is explained in chapters 15–17 of Peebles (1993).
  9. ^ Misner, Charles W. (1968). "The isotropy of the universe". Astrophysical Journal 151: 431. 
  10. ^ a b Misner, Charles; Thorne, Kip S. and Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman, pp. 489–490, 525–526. ISBN 0-7167-0344-0. 
  11. ^ Weinberg, Steven (1971). Gravitation and Cosmology. John Wiley, pp. 740, 815. ISBN 0-471-92567-5. 
  12. ^ Lemaître, Georges (1933). "The expanding universe". Ann. Soc. Sci. Bruxelles 47A: 49. , English in Gen. Rel. Grav. 29:641-680, 1997.
  13. ^ R. C. Tolman (1934). Relativity, Thermodynamics, and Cosmology. Oxford: Clarendon Press. LCCN 340-32023.  Reissued (1987) New York: Dover ISBN 0-486-65383-8.
  14. ^ Misner, Charles W. (1969). "Mixmaster universe". Phys. Rev. Lett. 22: 1071–74. 
  15. ^ Dicke, Robert H. (1970). Gravitation and the Universe. Philadelphia: American Philosopical Society. 
  16. ^ Dicke, Robert H.; P. J. E. Peebles (1979). "The big bang cosmology – enigmas and nostrums". ed. S. W. Hawking and W. Israel General Relativity: an Einstein Centenary Survey, Cambridge University Press. 
  17. ^ The importance of grand unification has waned somewhat since the early 1990s, as the simplest theories have been ruled out by proton decay experiments. However, many people still believe that a supersymmetric Grand Unified Theory is built into string theory, so it is still seen as a triumph for inflation that it is able to deal with these relics. See, e.g. Kolb and Turner (1988) and Raby, Stuart (2006). "Grand Unified Theories". ed. Bruce Hoeneisen Galapagos World Summit on Physics Beyond the Standard Model. 
  18. ^ 't Hooft, Gerard (1974). "Magnetic monopoles in Unified Gauge Theories". Nucl. Phys. B79: 276–84. 
  19. ^ Polyakov, Alexander M. (1974). "Particle spectrum in quantum field theory". JETP Lett. 20: 194–5. 
  20. ^ Zel'dovich, Ya. (1978). "On the concentration of relic monopoles in the universe". Phys. Lett. B79: 239–41. 
  21. ^ Preskill, John (1979). "Cosmological production of superheavy magnetic monopoles". Phys. Rev. Lett. 43: 1365. 
  22. ^ See, e.g. Yao, W.–M.; et al. (Particle Data Group). "Review of Particle Physics". J. Phys. G33: 1. 
  23. ^ de Sitter, Willem (1917). "Einstein's theory of gravitation and its astronomical consequences. Third paper". Monthly Notices of the Royal Astronomical Society 78: 3–28. 
  24. ^ Staorbinsky, Alexei A. (1980). "A new type of isotropic cosmological models without singularity". Phys. Lett. B91: 99–102. 
  25. ^ Kazanas, D. (1980). "Dynamics of the universe and spontaneous symmetry breaking". Astrophys. J. 241: L59–63. 
  26. ^ Sato, K. (1981). "Cosmological baryon number domain structure and the first order phase transition of a vacuum". Phys. Lett. B33: 66–70. 
  27. ^ See Linde (1990) and Mukhanov (2005).
  28. ^ Mukhanov, Viatcheslav F.; G. V. Chibisov (1981). "Quantum fluctuation and "nonsingular" universe". JETP Lett. 33: 532–5. 
  29. ^ Mukhanov, Viatcheslav F.; G. V. Chibisov (1982). "The vacuum energy and large scale structure of the universe". Sov. Phys. JETP 56: 258–65. 
  30. ^ See Guth (1997) for a description of the workshop.
  31. ^ Hawking, S.W. (1982). "The development of irregularities in a single bubble inflationary universe". Phys.Lett. B115: 295. 
  32. ^ Starobinsky, Alexei A. (1982). "Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations". Phys. Lett. B117: 175–8. 
  33. ^ Guth, A.H. (1982). "Fluctuations in the new inflationary universe". Phys. Rev. Lett. 49: 1110–3. 
  34. ^ Bardeen, James M.; Paul J. Steinhardt, Michael S. Turner (1983). "Spontaneous creation Of almost scale-free density perturbations in an inflationary universe". Phys. Rev. D28: 679. 
  35. ^ a b c d See, e.g. Spergel, D.N.; et al. (WMAP collaboration) (2006). "Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Implications for cosmology". 
  36. ^ Perturbations can be represented by Fourier modes of a given wavelength. Each Fourier mode is normally distributed (usually called Gaussian) with mean zero. Different Fourier components are uncorrelated. The variance of a mode depends only on its wavelength in such a way that within any given volume each wavelength contributes an equal amount of power to the spectrum of perturbations. Since the Fourier transform is in three dimensions, this means that the variance of a mode goes as k−3 to compensate for the fact that within any volume, the number of modes with a given wavenumber k goes as k3.
  37. ^ Tegmark, M.; et al. (SDSS collaboration) (August 2006). "Cosmological constraints from the SDSS luminous red galaxies". 
  38. ^ a b Steinhardt, Paul J. (2004). "Cosmological perturbations: Myths and facts". Mod. Phys. Lett. A19: 967–82. 
  39. ^ a b c Boyle, Latham A.; Paul J. Steinhardt and Neil Turok (2006). "Inflationary predictions for scalar and tensor fluctuations reconsidered". Phys. Rev. Lett. 96: 111301. 
  40. ^ a b Tegmark, Max (2005). "What does inflation really predict?". JCAP 0504: 001. 
  41. ^ This is known as a "red" spectrum, in analogy to redshift, because the spectrum has more power at longer wavelengths.
  42. ^ Spergel, D. N.; et al. (WMAP collaboration) (2003). "First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters". Astrophys. J. Suppl. 148: 175. 
  43. ^ See cosmic microwave background#Low multipoles for details and references.
  44. ^ Rosset, C.; (PLANCK-HFI collaboration) (2005). "Systematic effects in CMB polarization measurements". Exploring the universe: Contents and structures of the universe (XXXIXth Rencontres de Moriond). 
  45. ^ Loeb, A.; and M. Zaldarriaga (2004). "Measuring the small-scale power spectrum of cosmic density fluctuations through 21 cm tomography prior to the epoch of structure formation". Phys. Rev. Lett. 92: 211301. 
  46. ^ Technically, these conditions are that the logarithmic derivative of the potential, ε = (1 / 2)(V' / V)2 and second derivative η = V'' / V − (1 / 2)(V' / V)2 are small, where V is the potential and the equations are written in reduced Planck units. See, e.g. Liddle and Lyth (2000).
  47. ^ Linde, Andrei D. (1983). "Chaotic inflation". Phys. Lett. B129: 171–81. 
  48. ^ Technically, this is because the inflaton potential is expressed as a Taylor series in φ/mPl, where φ is the inflaton and mPl is the Planck mass. While for a single term, such as the mass term mφ4(φ/mPl)2, the slow roll conditions can be satisfied for φ much greater than mPl, this is precisely the situation in effective field theory in which higher order terms would be expected to contribute and destroy the conditions for inflation. The absence of these higher order corrections can be seen as another sort of fine tuning. See e.g. Alabidi, Laila; and David H. Lyth (2006). "Inflation models and observation". JCAP 0605: 016. 
  49. ^ See, e.g. Lyth, David H. (1997). "What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?". Phys. Rev. Lett. 78: 1861–3. arXiv:hep-ph/9606387. 
  50. ^ Brandenberger, Robert H. (Nov 2004). "Challenges for inflationary cosmology". 10th International Symposium on Particles, Strings and Cosmology. 
  51. ^ a b Vilenkin, Alexander (1983). "The birth of inflationary universes". Phys. Rev. D27: 2848. 
  52. ^ A. Linde (1986). "Eternal chaotic inflation". Mod. Phys. Lett. A1.  A. Linde (1986). "Eternally existing self-reproducing chaotic inflationary universe". Phys. Lett. B175. 
  53. ^ A. Borde, A. Guth and A. Vilenkin (2003). "Inflationary space-times are incomplete in past directions". Phys. Rev. Lett. 90. 
  54. ^ A. Borde (1994). "Open and closed universes, initial singularities and inflation". Phys. Rev. D50. 
  55. ^ A. Borde and A. Vilenkin (1994). "Eternal inflation and the initial singularity". Phys. Rev. Lett. 72. 
  56. ^ Linde (2005, §V).
  57. ^ Carroll, Sean M. (2005). "Does inflation provide natural initial conditions for the universe?". Gen. Rel. Grav. 37: 1671–4. 
  58. ^ Carroll, Sean M.. "Spontaneous inflation and the origin of the arrow of time". 
  59. ^ Anthony Aguirre, Steven Gratton, Inflation without a beginning: A null boundary proposal, Phys.Rev. D67 (2003) 083515, [1]
  60. ^ Anthony Aguirre, Steven Gratton, Steady-State Eternal Inflation, Phys.Rev. D65 (2002) 083507, [2]
  61. ^ J. Hartle and S. W. Hawking, "Wave function of the universe", Phys. Rev. D28, 2960 (1983). See also Hawking (1998).
  62. ^ Hawking (1998), p. 129. Wikiquote
  63. ^ D.N. Page, "Inflation does not explain time asymmetry", Nature, 304, 39 (1983) see also Roger Penrose's book The Road to Reality: A Complete Guide to the Laws of the Universe.
  64. ^ Hawking, S. W.; Don. N. Page (1988). "How probable is inflation?" B298: 789. 
  65. ^ Dyson, Lisa; Matthew Kleban and Leonard Susskind (2002). "Disturbing implications of a cosmological constant". JHEP 0210: 011. 
  66. ^ Albrecht, Andreas; Lorenzo Sorbo (2004). "Can the universe afford inflation?". Physical Review D70: 063528. 
  67. ^ Martin, Jerome; and Robert H. Brandenberger (2001). "The trans-Planckian problem of inflationary cosmology". Phys. Rev. D63: 123501. 
  68. ^ See Kolb and Turner (1988) or Mukhanov (2005).
  69. ^ Kofman, Lev (1994). "Reheating after inflation". Phys. Rev. Lett. 73: 3195–3198. 
  70. ^ Robert H. Brandenberger, "A Status Review of Inflationary Cosmology", proceedings Journal-ref: BROWN-HET-1256 (2001), (available from arXiv:hep-ph/0101119 v1 11 Jan 2001)
  71. ^ Andrei Linde, "Prospects of Inflation", Physica Scripta Online (2004) (available from arXiv:hep-th/0402051 )
  72. ^ Blanco-Pallido et al. , "Racetrack inflation", (2004) (available from arXiv:hep-th/0406230 )
  73. ^ Kachru, Shamit; Renata Kallosh, Andrei Linde, Juan M. Maldacena, Liam McAllister and Sandip P. Trivedi (2003). "Towards inflation in string theory". JCAP 0310: 013. 
  74. ^ Robert H. Brandenberger and C. Vafa, Superstrings in the early universe, Nucl. Phys. B316, 391 (1989)
  75. ^ Thorsten Battefeld and Scott Watson, String Gas Cosmology, Rev. Mod. Phys 78, 435-454 (2006)

The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. ... The Friedman equations relate various cosmological parameters within the context of general relativity. ... MCMXC redirects here; for the Enigma album, see MCMXC a. ... In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, usually a neutral pion and a positron. ... This article or section is in need of attention from an expert on the subject. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... The Particle Data Group is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. ... The Particle Data Group is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. ... Fourier series are a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ... The wavelength is the distance between repeating units of a wave pattern. ... The normal distribution, also called Gaussian distribution by scientists (named after Carl Friedrich Gauss due to his rigorous application of the distribution to astronomical data (Havil, 2003)), is a continuous probability distribution of great importance in many fields. ... In applied mathematics and physics, the spectral density is a general concept applied to a signal which may have any physical dimensions or none at all. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... WMAP image of the CMB anisotropy,Cosmic microwave background radiation(June 2003) The cosmic microwave background radiation (CMB) is a form of electromagnetic radiation that fills the whole of the universe. ... In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f′/f where f′ is the derivative of f. ... // In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... The inflaton is the generic name of the unidentified scalar field (and its associated particle), that may be responsible for an episode of inflation in the very early universe. ... arXiv (pronounced archive, as if the X were the Greek letter χ) is an archive for electronic preprints of scientific papers in the fields of physics, mathematics, computer science and quantitative biology which can be accessed via the Internet. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... The Road to Reality is a book by the British mathematical physicist Roger Penrose, published in 2004. ... arXiv (pronounced archive, as if the X were the Greek letter χ) is an archive for electronic preprints of scientific papers in the fields of physics, mathematics, computer science and quantitative biology which can be accessed via the Internet. ... arXiv (pronounced archive, as if the X were the Greek letter χ) is an archive for electronic preprints of scientific papers in the fields of physics, mathematics, computer science and quantitative biology which can be accessed via the Internet. ... arXiv (pronounced archive, as if the X were the Greek letter χ) is an archive for electronic preprints of scientific papers in the fields of physics, mathematics, computer science and quantitative biology which can be accessed via the Internet. ...

References

  • Guth, Alan (1997). The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus. ISBN 0-201-32840-2. 
  • Hawking, Stephen (1998). A Brief History of Time. Bantam. ISBN 0-553-38016-8. 
  • Kolb, Edward; Michael Turner (1988). The Early Universe. Addison-Wesley. ISBN 0-201-11604-9. 
  • Linde, Andrei (1990). Particle Physics and Inflationary Cosmology. Chur, Switzerland: Harwood. 
  • Linde, Andrei (2005) "Inflation and String Cosmology," eConf C040802 (2004) L024; J. Phys. Conf. Ser. 24 (2005) 151–60; arXiv:hep-th/0503195 v1 2005-03-24.
  • Liddle, Andrew; David Lyth (2000). Cosmological Inflation and Large-Scale Structure. Cambridge. ISBN 0-521-57598-2. 
  • Lyth, David H. (1999). "Particle physics models of inflation and the cosmological density perturbation". Phys. Rept. 314: 1–146. 
  • Mukhanov, Viatcheslav (2005). Physical Foundations of Cosmology. Cambridge University Press. ISBN 0-521-56398-4. 
  • Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press. ISBN 0-691-01933-9. 

Alan Harvey Guth (born February 27, 1947) is a physicist and cosmologist. ... Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ... Andrei Linde is an American physicist and professor of Physics at Californias Stanford University. ... arXiv (pronounced archive, as if the X were the Greek letter χ) is an archive for electronic preprints of scientific papers in the fields of physics, mathematics, computer science and quantitative biology which can be accessed via the Internet. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... March 24 is the 83rd day of the year (84th in leap years) in the Gregorian calendar. ... Philip James Edwin Peebles (born April 25, 1935) is an Canadian-American astronomer. ...

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