2.3 Expansion law and age of the
Universe
Equation (18) has the following
analytic solutions in several simple but practically important
cases.
- 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.