  We investigate the circumstances under which cosmic inflation can arise from
very inhomogeneous initial conditions using numerical relativity simulations.
Previous studies have not considered cases with non-zero momentum density due
to technical challenges with solving the coupled Einstein constraint equations.
Here we address these, introducing and comparing several different ways of
constructing cosmological initial conditions with inhomogeneous scalar field
and time derivative profiles. We evolve such initial conditions with large
inhomogeneities in both single- and two-field inflationary models. We study
cases where the initial gradient and kinetic energy are much larger than the
inflationary energy scale, and black holes can form, as well as cases where the
initial scalar potential energy is comparable, as in scenarios where inflation
occurs at nearly Planckian densities, finding large-field inflation to be
generally robust. We consider examples of initial conditions where a large
scalar field velocity towards non-inflationary values would prevent inflation
from occurring in the homogeneous case, finding that the addition of large
gradients in the scalar field can actually dilute this effect, with the
increased expansion and non-vanishing restoring force leading to inflation.
