Editing Einstein field equations (section)

== Cosmological constant ==
{{Main|Cosmological constant}}

In the Einstein field equations
<math display="block">G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu} \,,</math>
the term containing the cosmological constant {{math|Λ}} was absent from the version in which he originally published them.  Einstein then included the term with the cosmological constant to allow for a [[static universe|universe that is not expanding or contracting]]. This effort was unsuccessful because:
* any desired steady state solution described by this equation is unstable, and
* observations by [[Edwin Hubble]] showed that our universe is [[expanding universe|expanding]].

Einstein then abandoned {{math|Λ}}, remarking to [[George Gamow]] "that the introduction of the cosmological term was the biggest blunder of his life".<ref name = gamow>{{cite book| last = Gamow| first = George| author-link = George Gamow| title = My World Line : An Informal Autobiography| publisher = [[Viking Adult]]| date = April 28, 1970| isbn = 0-670-50376-2| url = http://www.jb.man.ac.uk/~jpl/cosmo/blunder.html| access-date = 2007-03-14 }}</ref>

The inclusion of this term does not create inconsistencies. For many years the cosmological constant was almost universally assumed to be zero. More recent [[astronomy|astronomical]] observations have shown an [[accelerating expansion of the universe]], and to explain this a positive value of {{math|Λ}} is needed.<ref name=wahl>{{cite news |last=Wahl |first=Nicolle |date=2005-11-22 |title=Was Einstein's 'biggest blunder' a stellar success? |url=http://www.news.utoronto.ca/bin6/051122-1839.asp |publisher =University of Toronto |work=News@UofT |archive-url=https://web.archive.org/web/20070307191343/http://www.news.utoronto.ca/bin6/051122-1839.asp <!-- Bot retrieved archive --> |archive-date=2007-03-07 }}</ref><ref name= turner>
{{cite journal
 |last=Turner |first=Michael S.
 |s2cid=16669258
 |date=May 2001
 |title=Making Sense of the New Cosmology
 |journal=Int. J. Mod. Phys. A
 |volume=17|issue=S1
 |pages=180–196
 |doi=10.1142/S0217751X02013113
 |arxiv=astro-ph/0202008|bibcode = 2002IJMPA..17S.180T
}}</ref> The effect of the cosmological constant is negligible at the scale of a galaxy or smaller.

Einstein thought of the cosmological constant as an independent parameter, but its term in the field equation can also be moved algebraically to the other side and incorporated as part of the stress–energy tensor:
<math display="block">T_{\mu \nu}^\mathrm{(vac)} = - \frac{\Lambda}{\kappa} g_{\mu \nu} \,.</math>

This tensor describes a [[vacuum state]] with an [[vacuum energy|energy density]] {{math|''ρ''{{sub|vac}}}} and isotropic pressure {{math|''p''{{sub|vac}}}} that are fixed constants and given by
<math display="block">\rho_\mathrm{vac} = - p_\mathrm{vac} = \frac{\Lambda}{\kappa},</math>
where it is assumed that {{math|Λ}} has SI unit m{{sup|−2}} and {{math|''κ''}} is defined as above.

The existence of a cosmological constant is thus equivalent to the existence of a vacuum energy and a pressure of opposite sign. This has led to the terms "cosmological constant" and "vacuum energy" being used interchangeably in general relativity.