cosmological constant - Cosmological constant problem

A constant introduced by Einstein into equations of general relativity to give a static model of the universe, later claimed by him to be a mistake; symbol ?; sign unknown; size uncertain, but less than 10^?25 kg/m³; often assumed to be zero. In cosmology, the value and sign are related to the expansion or contraction of the universe.

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. The discovery of cosmic acceleration in the 1990s has, however, renewed interest in a cosmological constant. The constant is proportional to the energy density of the vacuum ρvac:

where:

G is the gravitational constant c is the speed of light in vacuum

The term can be positive, negative, or zero. 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. This normalised cosmological constant 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. To counteract this possibility, Einstein added the cosmological constant.

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.

Since it no longer seemed to be needed, Einstein abandoned the cosmological constant and called it the "biggest blunder" of his life. 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. 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, or 10, or 10, or about 10-120 in reduced Planck units.

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. 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 infinitesimal cosmological constant observed in cosmology from particle physics. Weinberg demonstrated 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.

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. 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." "Interacting dark energy in f(R) gravity" - a relativistically covariant model of a variable cosmological constant, based on the principle of least action. News story:More evidence for dark energy being the cosmological constant