Mass-dominated Expansion of the Universe
In the current era, mass is dominant over radiation as a determiner of the expansion of the universe, whereas early times in the big bang were radiation-dominated. Some insight into the expansion can be obtained from a Newtonian expansion model which leads to a simplified version of the Friedman equation. Only recently have we been dealing with the fact that "dark energy" may be the dominant factor in the present expansion of the universe, but the examination of the mass-dominated expansion is important in providing insight about the current universe.
The simplified expansion equation is expressed in terms of the dimensionless scale factor R for the universe.
and putting the equation in a form where it can be integrated and expressed in terms of the Hubble time tH
Then for the present time R=R0=1 the expansion time is
and the scale factor R is given by
Carroll & Ostlie