Editing Scale factor (cosmology) (section)

{{Short description|Expansion of the universe parameter}}
The [[expansion of the universe]] is parametrized by a [[dimensionless]] '''scale factor''' <math>a </math>. Also known as the '''cosmic scale factor''' or sometimes the '''Robertson–Walker scale factor''',<ref name=Weinberg_Cosmology>{{cite book |url=https://books.google.com/books?id=48C-ym2EmZkC&pg=PA3 |author=Steven Weinberg |title=Cosmology |publisher=[[Oxford University Press]] |page=3 |date=2008 |isbn=978-0-19-852682-7}}</ref> this is a key parameter of the [[Friedmann equations]].

In the early stages of the [[Big Bang]], most of the energy was in the form of radiation, and that radiation was the dominant influence on the expansion of the universe. Later, with cooling from the expansion the roles of matter and radiation changed and the universe entered a matter-dominated era. Recent results suggest that we have already entered an era dominated by [[dark energy]], but examination of the roles of matter and radiation are most important for understanding the early universe.

Using the dimensionless scale factor to characterize the expansion of the universe, the effective energy densities of radiation and matter scale differently. This leads to a '''radiation-dominated era''' in the very early universe but a transition to a '''matter-dominated era''' at a later time and, since about 4 billion years ago, a subsequent '''dark-energy-dominated era'''.<ref name="Frieman">{{Cite journal|last1=Frieman|first1=Joshua A.|last2=Turner|first2=Michael S.|last3=Huterer|first3=Dragan|date=2008-01-01|title=Dark Energy and the Accelerating Universe|journal=Annual Review of Astronomy and Astrophysics|volume=46|issue=1|pages=385–432|arxiv=0803.0982|bibcode=2008ARA&A..46..385F|doi=10.1146/annurev.astro.46.060407.145243|s2cid=15117520}}</ref>{{refn|1= <ref name="Frieman" /> p. 6: "The Universe has gone through three distinct eras: radiation-dominated, ''z'' ≳ 3000; matter-dominated, 3000 ≳ ''z'' ≳ 0.5; and dark-energy dominated, ''z'' ≲ 0.5. The evolution of the scale factor is controlled by the dominant energy form: a(t) ∝ t<sup>2/3(1+w)</sup> (for constant ''w''). During the radiation-dominated era, a(t) ∝ t<sup>1/2</sup>; during the matter-dominated era, a(t) ∝ t<sup>2/3</sup>; and for the dark-energy-dominated era, assuming ''w'' = −1, asymptotically a(t) ∝ exp(Ht)."<br />
p. 44: "Taken together, all the current data provide strong evidence for the existence of dark energy; they constrain the fraction of critical density contributed by dark energy, 0.76 ± 0.02, and the equation-of-state parameter, ''w'' ≈ −1 ± 0.1 (stat) ±0.1 (sys), assuming that ''w'' is constant. This implies that the Universe began accelerating at redshift ''z'' ∼ 0.4 and age ''t'' ∼ 10 Gyr. These results are robust – data from any one method can be removed without compromising the constraints – and they are not substantially weakened by dropping the assumption of spatial flatness."|group="notes"}}