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The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] 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 for a static universe: gravity would cause a universe that was ...
The value of R as a function of time t depends upon k and the cosmological constant Λ. [151] The cosmological constant represents the energy density of the vacuum of space and could be related to dark energy. [98] The equation describing how R varies with time is known as the Friedmann equation after its inventor, Alexander Friedmann. [154]
For many years the cosmological constant was almost universally assumed to be zero. More recent astronomical observations have shown an accelerating expansion of the universe, and to explain this a positive value of Λ is needed. [18] [19] The effect of the cosmological constant is negligible at the scale of a galaxy or smaller.
In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical value of zero-point energy suggested by quantum field theory.
where is the Einstein tensor, is the cosmological constant (sometimes taken to be zero for simplicity), is the metric tensor, is a constant, and is the stress–energy tensor. The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime ...
One of the simplest explanations is that it is a “cosmological constant” – a result of the energy of empty space itself – an idea introduced by Albert Einstein.
The Einstein field equation is often written as + =, with a so-called cosmological constant term. However, it is possible to move this term to the right hand side and absorb it into the stress–energy tensor T a b {\displaystyle T^{ab}} , so that the cosmological constant term becomes just another contribution to the stress–energy tensor.
A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter.It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe.