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Cosmological constant was first proposed by Einstein.
The cosmological constant was suggested by 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.
The cosmological constant appears in Einstein's modified field equation in the form
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 ? 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.
The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ?vac (and an associated pressure). In this context it is commonly defined with a proportionality factor of 8p: ? = 8p?vac, 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".
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 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 calledO?. In a flat universeO? 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.
General relativity and the cosmological constant.
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.
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. These sorts of small contractions are inevitable, due to the uneven distribution of matter throughout the universe.
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 , 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.
Cosmological constant problem.
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.
One possible explanation for the small but non-zero value was noted by Steven Weinberg in 1987. 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.
As was only recently seen, by works of 't Hooft, Susskind and others, a positive cosmological constant has surprising consequences, such as a finite maximum Entropy of the observable universe .
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." 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."
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