Editing Cosmological constant (section)

== History ==
The cosmological constant was originally introduced in [[Albert Einstein|Einstein's]] 1917 paper entitled “''Cosmological considerations in the General Theory of Relativity''”.<ref name=":0" /> Einstein included the cosmological constant as a term in his [[Einstein field equations|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 initially non-expanding to contract. To counteract this possibility, Einstein added the cosmological constant.<ref name="Rugh 2001 3"/> However, Einstein was not happy about adding this cosmological term. He later stated that "Since I introduced this term, I had always a bad conscience. ... I am unable to believe that such an ugly thing is actually realized in nature".<ref>{{Cite journal |last=Kirshner |first=Robert P. |date=2004-01-06 |title=Hubble's diagram and cosmic expansion |journal=Proceedings of the National Academy of Sciences |language=en |volume=101 |issue=1 |pages=8–13 |doi=10.1073/pnas.2536799100 |doi-access=free |issn=0027-8424 |pmc=314128 |pmid=14695886}}</ref> Einstein's static universe is unstable against matter density perturbations.<ref>{{Cite journal |last=Eddington |first=A. S. |date=1930-05-09 |title=On the Instability of Einstein's Spherical World |journal=Monthly Notices of the Royal Astronomical Society |volume=90 |issue=7 |pages=668–678 |doi=10.1093/mnras/90.7.668 |doi-access=free |issn=0035-8711}}</ref> Furthermore, without the cosmological constant Einstein could have found the expansion of the universe before Hubble's observations.<ref name=":1">{{Cite journal |last=Hubble |first=Edwin |date=1929-03-15 |title=A relation between distance and radial velocity among extra-galactic nebulae |journal=Proceedings of the National Academy of Sciences |language=en |volume=15 |issue=3 |pages=168–173 |doi=10.1073/pnas.15.3.168 |doi-access=free |issn=0027-8424 |pmc=522427 |pmid=16577160|bibcode=1929PNAS...15..168H }}</ref>

In 1929, not long after Einstein developed his static theory, observations by [[Edwin Hubble]]<ref name=":1" /> indicated that the universe appears to be expanding; this was consistent with a cosmological solution to the original general relativity equations that had been found by the mathematician [[Alexander Alexandrovich Friedmann|Alexander Friedmann]], working on the Einstein equations of general relativity. Einstein reportedly referred to his failure to accept the validation of his equations—when they had predicted the expansion of the universe in theory, before it was demonstrated in observation of the cosmological [[redshift]]—as his "biggest blunder" (according to [[George Gamow]]).<ref name="Biggest Blunder" />

It transpired that adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the [[equilibrium point|equilibrium]] is unstable: if the universe expands slightly, then the expansion releases [[vacuum energy]], which causes yet more expansion. Likewise, a universe that contracts slightly will continue contracting.<ref>{{harvp|Ryden|2003|p=59}}</ref>

However, the cosmological constant remained a subject of theoretical and empirical interest. Empirically, the cosmological data of recent decades strongly suggest that our universe has a positive cosmological constant.<ref name="1998 Discovery"/> The explanation of this small but positive value is a remaining theoretical challenge, the so-called [[cosmological constant problem]].

Some early generalizations of Einstein's gravitational theory, known as [[classical unified field theories]], either introduced a cosmological constant on theoretical grounds or found that it arose naturally from the mathematics. For example, [[Arthur Eddington]] claimed that the cosmological constant version of the vacuum field equation expressed the "[[epistemology|epistemological]]" property that the universe is "self-[[gauge theory|gauging]]", and [[Erwin Schrödinger]]'s pure-[[affine connection|affine]] theory using a simple [[History of variational principles in physics|variational principle]] produced the field equation with a cosmological term.

In 1990s, [[Saul Perlmutter]] at Lawrence Berkeley National Laboratory, [[Brian Schmidt]] of the Australian National University and [[Adam Riess]] of the Space Telescope Science Institute were searching for type Ia supernovae. At that time, they expected to observe the deceleration of the supernovae caused by gravitational attraction of mass according to Einstein's gravitational theory. The first reports published in July 1997 from the Supernova Cosmology Project used the supernova observation to support such deceleration hypothesis. But soon they found that supernovae were accelerating away. Both teams announced this surprising result in 1998. It implied the universe is undergoing accelerating expansion. The cosmological constant is needed to explain such acceleration.<ref>{{Cite journal |last1=Riess |first1=Adam G. |last2=Filippenko |first2=Alexei V. |last3=Challis |first3=Peter |last4=Clocchiatti |first4=Alejandro |last5=Diercks |first5=Alan |last6=Garnavich |first6=Peter M. |last7=Gilliland |first7=Ron L. |last8=Hogan |first8=Craig J. |last9=Jha |first9=Saurabh |last10=Kirshner |first10=Robert P. |last11=Leibundgut |first11=B. |last12=Phillips |first12=M. M. |last13=Reiss |first13=David |last14=Schmidt |first14=Brian P. |last15=Schommer |first15=Robert A. |date=1998 |title=Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant |url=https://iopscience.iop.org/article/10.1086/300499 |journal=The Astronomical Journal |volume=116 |issue=3 |pages=1009–1038 |doi=10.1086/300499|arxiv=astro-ph/9805201 |bibcode=1998AJ....116.1009R }}</ref> Following this discovery, the cosmological constant was reinserted in the general relativity equations.

=== Sequence of events 1915–1998 ===
* In 1915, Einstein publishes his equations of general relativity, without a cosmological constant {{math|Λ}}.
* In 1917, Einstein adds the parameter {{math|Λ}} to his equations when he realizes that his theory implies a dynamic universe for which space is a function of time. He then gives this constant a value that makes his Universe model remain static and eternal (Einstein static universe).
* In 1922, the Russian physicist [[Alexander Friedmann]] mathematically shows that Einstein's equations (whatever {{math|Λ}}) remain valid in a dynamic universe.
* In 1927, the Belgian astrophysicist [[Georges Lemaître]] shows that the Universe is expanding by combining general relativity with astronomical observations, those of Hubble in particular.
* In 1931, Einstein accepts the theory of an expanding universe and proposes, in 1932 with the Dutch physicist and astronomer [[Willem de Sitter]], a model of a continuously expanding universe with zero cosmological constant (Einstein–de Sitter spacetime).
* In 1998, two teams of astrophysicists, the [[Supernova Cosmology Project]] and the [[High-Z Supernova Search Team]], carried out measurements on distant supernovae which showed that the speed of galaxies' recession in relation to the [[Milky Way]] increases over time. The universe is in accelerated expansion, which requires having a strictly positive {{math|Λ}}. The universe would contain a mysterious dark energy producing a repulsive force that counterbalances the gravitational braking produced by the matter contained in the universe (see ''[[Standard cosmological model]]''). {{pb}} For this work, Perlmutter, Schmidt, and Riess jointly received the [[Nobel Prize in Physics]] in 2011.