  We study the onset of inflation in 3+1 dimensional cosmologies with an
inflationary potential $U$ satisfying $0 < \Lambda_1 \leq U \leq \Lambda_2$,
matter satisfying the dominant and strong energy conditions, and with spatial
slices that can be foliated by 2-dimensional surfaces that are orbits under an
isometry group. Assuming an initial Cauchy slice with positive mean curvature
everywhere, we show, via mean curvature flow, that there exists a family of
spatial slices parameterized by $\lambda$, whose volume grows between the flat
slicings in de Sitter spaces with cosmological constants $\Lambda_1$ and
$\Lambda_2$. In particular, inflationary expansion indeed occurs in this
setting with inhomogeneous initial conditions. Finally, we apply this
"inflationary time coordinate" $\lambda$ to study asymptotics of the variation
in the metric, the average stress-energy tensor, and the dynamics of an
inflaton field on a spatial slice.
