2.3 Expansion law and age of the Universe
Equation (18) has the following analytic solutions in several simple but practically important
- Einstein–de Sitter model ():
- Open model with vanishing cosmological constant ():
- Spatially-flat model with cosmological constant ():
In the above, denotes the present age of the Universe,
and we adopt the initial condition that at . The expression clearly indicates that
increases as decreases and/or increases. Figure 1 plots the scale factor as a function of
, and Table 1 summarizes the age of the Universe.
Figure 1: Evolution of the cosmic scale factor as a function of . The present value
of the scale factor is set to unity; solid line: , dotted line: ,
dot-dashed line: , long dashed line: , short dashed line: .