## Saturday, 10 March 2012

### Cosmological constant

Main article: Cosmological constant
For more details on this topic, see Equation of state (cosmology).

The simplest explanation for dark energy is that it is simply the "cost of having space": that is, a volume of space has some intrinsic, fundamental energy. This is the cosmological constant, sometimes called Lambda (hence Lambda-CDM model) after the Greek letter Λ, the symbol used to mathematically represent this quantity.

Since energy and mass are related by E = mc2, Einstein's theory of general relativity predicts that it will have a gravitational effect. It is sometimes called a vacuum energy because it is the energy density of empty vacuum. In fact, most theories of particle physics predict vacuum fluctuations that would give the vacuum this sort of energy.

This is related to the Casimir Effect, in which there is a small suction into regions where virtual particles are geometrically inhibited from forming (e.g. between plates with tiny separation).

The cosmological constant is estimated by cosmologists to be on the order of 10−29g/cm³, or about 10−120 in reduced Planck units. However, particle physics predicts a natural value of 1 in reduced Planck units, a large discrepancy which is still lacking in explanation.

The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate. The reason why a cosmological constant has negative pressure can be seen from classical thermodynamics; Energy must be lost from inside a container to do work on the container.

A change in volume dV requires work done equal to a change of energy −p dV, where p is the pressure. But the amount of energy in a box of vacuum energy actually increases when the volume increases (dV is positive), because the energy is equal to ρV, where ρ (rho) is the energy density of the cosmological constant. Therefore, p is negative and, in fact, p = −ρ.

A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum, more than 100 orders of magnitude too large. 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 does not help. The present scientific consensus amounts to extrapolating the empirical evidence where it is relevant to predictions, and fine-tuning theories until a more elegant solution is found. Philosophically, our most elegant solution may be to say that if things were different, we would not be here to observe anything — the anthropic principle.

Technically, this amounts to checking theories against macroscopic observations. Unfortunately, as the known error-margin in the constant predicts the fate of the universe more than its present state, many such "deeper" questions remain unknown.

Another problem arises with inclusion of the cosmic constant in the standard model: i.e., the appearance of solutions with regions of discontinuities (see classification of discontinuities for three examples) at low matter density.

Discontinuity also affects the past sign of the pressure assigned to the cosmic constant, changing from the current negative pressure to attractive, as one looks back towards the early Universe.

A systematic, model-independent evaluation of the supernovae data supporting inclusion of the cosmic constant in the standard model indicates these data suffer systematic error. The supernovae data are not overwhelming evidence for an accelerating Universe expansion which may be simply gliding.

A numerical evaluation of WMAP and supernovae data for evidence that our local group exists in a local void with poor matter density compared to other locations, uncovered possible conflict in the analysis used to support the cosmic constant.

These findings should be considered shortcomings of the standard model, but only when a term for vacuum energy is included.

In spite of its problems, the cosmological constant is in many respects the most economical solution to the problem of cosmic acceleration. One number successfully explains a multitude of observations. Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant as an essential feature.

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