Beginning inflation in an inhomogeneous universe

TL;DR

This study demonstrates through numerical relativity that inflation can originate from highly inhomogeneous initial conditions, including regions with large density contrasts, provided the scalar field variations are within the inflationary potential plateau.

Contribution

It provides the first numerical evidence that inflation can start in a universe with significant initial inhomogeneities and black hole formation, expanding the initial conditions compatible with inflation.

Findings

Inflation occurs if scalar field variations are within the flat potential region.

Overdense regions can collapse into black holes while underdense regions continue expanding.

Inflation can begin even when inhomogeneities are on the order of the initial Hubble length.

Abstract

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.