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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 term Friedmann equation sometimes is used only for the first equation. [3] In these equations, R(t) is the cosmological scale factor, is the Newtonian constant of gravitation, Λ is the cosmological constant with dimension length −2, ρ is the energy density and p is the isotropic pressure.
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
A free (=) scalar field has =, and one with vanishing kinetic energy is equivalent to a cosmological constant: =. Any equation of state in between, but not crossing the w = − 1 {\displaystyle w=-1} barrier known as the Phantom Divide Line (PDL), [ 2 ] is achievable, which makes scalar fields useful models for many phenomena in cosmology.
The "cosmological constant" is a constant term that can be added to Einstein field equations of general relativity.If considered as a "source term" in the field equation, it can be viewed as equivalent to the mass of empty space (which conceptually could be either positive or negative), or "vacuum energy".
The cosmological constant is given the symbol Λ, and, considered as a source term in the Einstein field equation, can be viewed as equivalent to a "mass" of empty space, or dark energy. Since this increases with the volume of the universe, the expansion pressure is effectively constant, independent of the scale of the universe, while the other ...
Substituting these conditions to the Friedmann equation gives [15] = = (), where / is the reduced Hubble constant. If the cosmological constant were actually zero, the critical density would also mark the dividing line between eventual recollapse of the universe to a Big Crunch, or unlimited expansion.
The constants and are Newton's gravitational constant and the speed of light, respectively. Cosmologists often simplify this equation by defining a critical density, ρ c {\displaystyle \rho _{c}} . For a given value of H {\displaystyle H} , this is defined as the density required for a flat universe, i.e. k = 0 {\displaystyle k=0} .