Beginning inflation in an inhomogeneous universe
  Using numerical solutions of the full Einstein field equations coupled to a
scalar inflaton field in 3+1 dimensions, we study the conditions under which a
universe that is initially expanding, highly inhomogeneous and dominated by
gradient energy can transition to an inflationary period. If the initial scalar
field variations are contained within a sufficiently flat region of the
inflaton potential, and the universe is spatially flat or open on average,
inflation will occur following the dilution of the gradient and kinetic energy
due to expansion. This is the case even when the scale of the inhomogeneities
is comparable to the initial Hubble length, and overdense regions collapse and
form black holes, because underdense regions continue expanding, allowing
inflation to eventually begin. This establishes that inflation can arise from
highly inhomogeneous initial conditions and solve the horizon and flatness
problems, at least as long as the variations in the scalar field do not include
values that exceed the inflationary plateau.
