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

Starting inflation from inhomogeneous initial conditions with momentum