3.1. The potential dominated state
Consider adding an additional scalar matter field
(the ``inflaton'') to
the cosmological model. In general the stress-energy tensor of this
field will depend on the space and time derivatives of the field as
well as the potential V().
In the limit where the potential
term dominates over the derivative terms the stress-energy tensor of
takes the form
which leads (by comparison with Eqn. 3) to
Solving Eqn. 2 gives
very different from the power law behavior in the SBB.
= -p = V.
(a) =
V. Because we are assuming
is negligible we also have
V = const.. Under
these circumstances H = const. and the Friedmann equation
gives exponential expansion:
