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Cosmological Constant and its Significance

Abdul Najeeb asked via Facebook:

Would you plz explain me what is a cosmological constant? When Einstein snubbed it as the "biggest blunder" in his life, what else is the real importance of the constant? Also what is cosmological acceleration and its’ effect on the constant…plz…but in simple words…plzzzz:)))))

Ans:

The cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe.

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Einstein abandoned the concept after the observation of the Hubble redshift indicated that the universe might not be stationary, as he had based his theory on the idea that the universe is unchanging.However, the discovery of cosmic acceleration in the 1990s has renewed interest in a cosmological constant.

{courtesy : Wikipedia}

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More on Cosmological constant

A constant introduced by Einstein  (1917) into the equations of general relativity to allow a steady state cosmological solution to the Einstein field equations. The constant was introduced before the concept of the Big Bang had been conceived, so an expanding or contracting universe  was regarded as physically implausible, leading Einstein to add as a "fudge factor." In theory, the constant can be derived from quantum field theory, but the derivation has not yet been performed. Einstein’s cosmological constant is equivalent to a vacuum energy density, which means it can be put on the left hand side of Einstein’s equations with the geometry (as Einstein did), or on the right hand side with the stress-energy, both forms being mathematically equivalent.

 

The value of in our present universe is not known, and may be zero, although there is some evidence for a nonzero value; a precise determination of this number will be one of the primary goals of observational cosmology in the near future.

The value of the cosmological constant is an empirical issue which will ultimately be settled by observation; meanwhile, physicists would like to develop an understanding of why the energy density of the vacuum has this value, whether it is zero or not. There are many effects which contribute to the total vacuum energy,
including the potential energy of scalar fields and the energy in “vacuum fluctuations” as predicted by quantum mechanics, as well as any fundamental cosmological constant.

image If the recent observational suggestions of a nonzero are confirmed, we will be faced with the additional task of inventing a theory which sets the vacuum energy to a very small value without setting it precisely to zero. In this case we may distinguish between a “true” vacuum which would be the state of lowest possible energy which simply happens to be nonzero, and a “false” vacuum, which would be a metastable state different from the actual state of lowest energy (which might well have = 0). Such a state could eventually decay into the true vacuum, although its lifetime could be much larger than the current age of the universe. A
final possibility is that the vacuum energy is changing with time — a dynamical cosmological “constant”. This alternative, which is sometimes called “quintessence”, would also be compatible with a true vacuum energy which was ultimately zero, although it appears to require a certain amount of fine-tuning to make it work.
No matter which of these possibilities, if any, is true, the ramifications of an accelerating universe for fundamental physics would be truly profound.

Read More at

  1.  http://relativity.livingreviews.org/Articles/lrr-2001-1/
  2. http://www.astro.ucla.edu/~wright/cosmo_constant.html
  3. http://www.scholarpedia.org/article/Cosmological_constant

Importance of Cosmological Constant

Understanding the unnaturally small size of the cosmological constant poses one of severest challenges for a theory of gravity. image At late times and for large distances, the apparent size of the cosmological constant is constrained to be extremely small in terms of the natural scale for gravity, the Planck mass. In contrast, no observations bound the value of the cosmological constant during the earliest stages of the universe, when corrections to the Einstein-Hilbert action were non-negligible, and its presence can lead to a richer family
of metrics. Among the solutions for a more general gravitational action, the presence of a positive  cosmological constant does not inevitably lead to a de Sitter expansion. Such solutions must still yield or evolve into a low energy theory in which the effective cosmological constant is small to be phenomenologically acceptable. If the characteristic scales on which these metrics vary are of extremely high energy or short distance, then it may be possible to integrate out such features to arrive at a slowly varying e®ective theory.
To determine whether an action for gravity, generalized beyond an Einstein-Hilbert term, admits these features | natural coefficients for the terms in the action and a rapid variation | we must ¯rst solve the highly non-linear field equations. This task is difficult even when only the next curvature corrections are added. In 3 + 1 dimensions, Horowitzand Wald and later Starobinsky [3] discovered oscillating solutions for actions that
included quadratic curvature terms but no cosmological constant. Numerical solutions were found in 4 + 1 dimensions in the presence of a cosmological constant and a scalar field, along with the quadratic curvature terms. In this latter scenario, metrics exist that depend periodically on the extra spatial coordinate so that choosing the size of the extra dimension to be the period produces a compact extra dimension without any fine-tunings or singularities. The parameters in the action ¯x the size of the extra dimension uniquely.
However, without an analytical approach it becomes di±cult to generalize these solutions to include an evolution in time. Without this freedom, it is di±cult to understand how a universe starting from a more general state can  find itself in one of these configurations.

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