**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
= -*p* = *V*.

Solving Eqn. 2 gives
(*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:

very different from the power law behavior in the SBB.