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Encyclopedia > Cosmological constant

In physical cosmology, 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. After the discovery of the Hubble redshift and the introduction of the expanding space paradigm, Einstein abandoned the concept. However, the discovery of cosmic acceleration in the 1990s has renewed interest in a cosmological constant. 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. ... â€œEinsteinâ€ redirects here. ... An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Hubbles law is the statement in astronomy that the redshift in light coming from distant galaxies is proportional to their distance. ... According to the Big Bang model, the universe developed from an extremely dense and hot state. ... The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of the universe. ...

The cosmological constant Λ appears in Einstein's modified field equation in the form This article or section is in need of attention from an expert on the subject. ...

$R_{mu nu} - {textstyle 1 over 2}R,g_{mu nu} + Lambda,g_{mu nu} = {8 pi G over c^4} T_{mu nu}$

where R and g pertain to the structure of spacetime, T pertains to matter (thought of as affecting that structure), and G and c are conversion factors which arise from using traditional units of measurement. When Λ is zero, this reduces to the original field equation of general relativity. When T is zero, the field equation describes empty space (the vacuum). Astronomical observations imply that the constant cannot exceed 10-46 km-2.[1] In differential geometry, the Ricci curvature tensor is (0,2)-valent tensor, obtained as a trace of the full curvature tensor. ... In general relativity, the metric tensor (or simply the metric) is the fundamental object of study. ... In physics, spacetime is any mathematical model that combines space and time into a single construct called the space-time continuum. ... This article is in need of attention from an expert on the subject. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... 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.[1] It is the speed of all electromagnetic... Look up Vacuum in Wiktionary, the free dictionary. ...

The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρvac (and an associated pressure). In this context it is commonly defined with a proportionality factor of 8π: Λ = 8πρvac, where modern unit conventions of general relativity are followed (otherwise factors of G and c would also appear). It is common to quote values of energy density directly, though still using the name "cosmological constant". 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 use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ... In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ...

A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of empty space; see dark energy and cosmic inflation for details. 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 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. ...

In lieu of the cosmological constant, cosmologists often quote the ratio between the energy density due to the cosmological constant and the current critical density of the universe. This ratio is usually called ΩΛ. In a flat universe ΩΛ corresponds to the fraction of the energy density of the Universe which is associated with the cosmological constant. Note that this definition is tied to the critical density of the present cosmological era: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the 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. ... 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. ...

## Contents

Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow, apparently, for a static universe: gravity would cause a universe which was initially at dynamical equilibrium to contract. To counteract this possibility, Einstein added the cosmological constant. However, soon after Einstein developed his static theory, observations by Edwin Hubble indicated that the universe appears to be expanding; this was consistent with a cosmological solution to the original general-relativity equations that had been found by the mathematician Friedman. This article or section is in need of attention from an expert on the subject. ... An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... Basic description The theory of a static universe is the rival theory to an expanding universe and all of its subvarieties. ... â€œEinsteinâ€ redirects here. ... Edwin Powell Hubble (November 20, 1889 â€“ September 28, 1953) was an American astronomer. ... Alexander Alexandrovich Friedman or Friedmann (ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€ ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€Ð¾Ð²Ð¸Ñ‡ Ð¤Ñ€Ð¸Ð´Ð¼Ð°Ð½) (June 16, 1888 â€“ September 16, 1925) was a Russian cosmologist and mathematician. ...

It is now thought that adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. In mathematics, the point is an equilibrium point for the differential equation if for all . ...

Since it no longer seemed to be needed, Einstein abandoned the cosmological constant and called it the "biggest blunder" of his life. (He may have been referring to his methodology rather than to the constant itself.) Ironically, the cosmological constant is still of interest, as observations made in the late 1990s of distance-redshift relations indicate that the expansion of the universe is accelerating. When combined with measurements of the cosmic microwave background radiation these implied a value of $Omega_{Lambda} simeq 0.7$[2], a result which has been supported and refined by more recent measurements. There are other possible causes of an accelerating universe, such as quintessence, but the cosmological constant is in most respects the most economical solution. Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant, which is measured to be on the order of 10-35s-2, or 10-47GeV4, or 10-29g/cm3, or about 10-120 in reduced Planck units. Look up Blunder in Wiktionary, the free dictionary. ... 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. ... The Accelerating universe is the idea that our universe is undergoing accelerated expansion: distant objects are receding from our galaxy with speeds that increase over time. ... In physics, quintessence is a hypothetical form of dark energy postulated as an explanation of observations of an accelerating universe. ... William of Ockham Occams razor (sometimes spelled Ockhams razor) is a principle attributed to the 14th-century English logician and Franciscan friar William of Ockham. ... A pie chart indicating the proportional composition of different energy-density components of the universe. ... // In physics, Planck units are physical units of measurement originally proposed by Max Planck. ...

Some early generalizations of Einstein's gravitational theory, known as classical unified field theories, either introduced a cosmological constant on theoretical grounds or found that it arose naturally from the mathematics. For example, Sir Arthur Stanley Eddington claimed that the cosmological constant version of the vacuum field equation expressed the "epistemological" property that the universe is "self-gauging", and Erwin Schrödinger's pure-affine theory using a simple variational principle produced the field equation with a cosmological term. This article is in need of attention. ... One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the English-speaking world. ... It has been suggested that Meta-epistemology be merged into this article or section. ... 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. ... Bust of SchrÃ¶dinger, in the courtyard arcade of the main building, University of Vienna, Austria. ... An affine connection is a connection on the tangent bundle of a differentiable manifold. ... A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a function or functional. ...

## Cosmological constant problem

Unsolved problems in physics: Why doesn't the zero-point energy of vacuum cause a large cosmological constant? What cancels it out?

A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum. This would need to be cancelled almost, but not exactly, by an equally large term of the opposite sign. Some supersymmetric theories require a cosmological constant that is exactly zero, which further complicates things. This is the cosmological constant problem, the worst problem of fine-tuning in physics: there is no known natural way to derive the tiny cosmological constant used in cosmology from particle physics. Image File history File links No higher resolution available. ... This is a list of some of the unsolved problems in physics. ... In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. ... Look up Vacuum in Wiktionary, the free dictionary. ... This is a list of some of the unsolved problems in physics. ... Quantum field theory (QFT) is the quantum theory of fields. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... This article or section is in need of attention from an expert on the subject. ... Fine Tuning is the name of XM Satellite Radios eclectic music channel. ... This article needs additional references or sources for verification. ... 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. ... 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. ...

One possible explanation for the small but non-zero value was noted by Steven Weinberg in 1987.[3] Weinberg explains that if the vacuum energy took different values in different domains of the universe, then observers would necessarily measure values similar to that which is observed: the formation of life-supporting structures would be suppressed in domains where the vacuum energy is much larger, and domains where the vacuum energy is much smaller would be comparatively rare. This argument depends crucially on the reality of a spatial distribution in the vacuum energy density. There is no evidence that the vacuum energy does vary, but it may be the case if, for example, the vacuum energy is (even in part) the potential of a scalar field such as the residual inflaton (also see quintessence). Critics note that these multiverse theories, when used as an explanation for fine-tuning, commit the inverse gamblers fallacy. Steven Weinberg (born May 3, 1933) is an American physicist. ... 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. ... Look up Quintessence in Wiktionary, the free dictionary. ... A multiverse (or meta-universe) is the hypothetical set of multiple possible universes (including our universe) that together comprise all of physical reality. ... The inverse gamblers fallacy is a tempting mistake in judgments of probability, comparable to the gamblers fallacy whence its name derives. ...

As was only recently seen, by works of 't Hooft, Susskind[4] and others, a positive cosmological constant has surprising consequences, such as a finite maximum entropy of the observable universe (see the holographic principle). Gerard t Hooft at Harvard University Gerardus (Gerard) t Hooft [ut-hooft] (The prefix â€™t is pronounced as â€˜utâ€™ and stands for â€˜hetâ€™) (born July 5, 1946) is a professor in theoretical physics at Utrecht University, The Netherlands. ... Leonard Susskind (born 1940[1]) is the Felix Bloch professor of theoretical physics at Stanford University in the field of string theory and quantum field theory. ... 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. ... 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 which lives in the boundary of that region. ...

More recent work has suggested the problem may be indirect evidence of a cyclic universe predicted by string theory. With every cycle of the universe (Big Bang then eventually a Big Crunch) taking about a trillion (1012) years, "the amount of matter and radiation in the universe is reset, but the cosmological constant is not. Instead, the cosmological constant gradually diminishes over many cycles to the small value observed today."[5] Critics respond that, as the authors acknowledge in their paper, the model “entails tuning” to “the same degree of tuning required in any cosmological model.” [6] The cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. ... 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... According to the Big Bang model, the universe developed from an extremely dense and hot state. ... This article is about the cosmological theory. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ...

To meet Wikipedias quality standards, this article or section may require cleanup. ... Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). ... In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress-energy tensor is a cosmological constant term. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... According to the Big Bang model, the universe developed from an extremely dense and hot state. ...

## References

1. ^ Christopher S. Kochanek (August 1996). ""Is There a Cosmological Constant?"". The Astrophysical Journal 466 (2): 638-659.
2. ^ See e.g. Detection of cosmic microwave background structure in a second field with the Cosmic Anisotropy Telescope, Baker, Joanne C.; Grainge, Keith; Hobson, M. P.; Jones, Michael E.; Kneissl, R.; Lasenby, A. N.; O'Sullivan, C. M. M.; Pooley, Guy; Rocha, G.; Saunders, Richard; Scott, P. F.; Waldram, E. M., Monthly Notices of the Royal Astronomical Society, Volume 308, Issue 4, pp. 1173-1178
3. ^ [Weinberg, S. 1987, "Anthropic Bound on the Cosmological Constant", PRL 59]
4. ^ Lisa Dyson, Matthew Kleban, Leonard Susskind: "Disturbing Implications of a Cosmological Constant"
5. ^ 'Cyclic universe' can explain cosmological constant, NewScientistSpace, 04 May 2006
6. ^ [Steinhardt and Turok, 1437]

### Further information

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Images and media from Commons
News stories from Wikinews
Learning resources from Wikiversity
• Michael, E., University of Colorado, Department of Astrophysical and Planetary Sciences, "The Cosmological Constant", [1]
• Ferguson, Kitty (1991). Stephen Hawking: Quest For A Theory of Everything, Franklin Watts. ISBN 0-553-29895-X.

Results from FactBites:

 Cosmological constant - Wikipedia, the free encyclopedia (1027 words) 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 lieu of the cosmological constant, cosmologists often quote the ratio between the energy density due to the cosmological constant and the current critical density of the universe. Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow, apparently, for a static universe.
 cosmological constant: Definition and Much More from Answers.com (1189 words) Because the cosmological constant has negative pressure, according to general relativity a positive cosmological constant — which means empty space has positive energy — causes the expansion of empty space to accelerate (see dark energy for details). Cosmologists generally describe the cosmological constant in units where unity would correspond to the value of the cosmological constant which would give a closed universe in the absence of matter. It is now thought that adding the cosmological constant to Einstein's equations does not lead to a universe at equilibrium because the equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion.
More results at FactBites »

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