Long-wavelength non-linear perturbations of a complex scalar field

TL;DR

This paper investigates the nonlinear evolution of superhorizon perturbations in a universe with a complex scalar field, providing solutions that aid in setting initial conditions for primordial black hole simulations.

Contribution

It derives second-order solutions for nonlinear scalar field perturbations in a complex scalar field universe, including explicit cases for quadratic and quartic potentials.

Findings

Explicit second-order solutions for scalar perturbations.

Solutions applicable to quadratic and quartic potentials.

Relevance for initial conditions in primordial black hole formation.

Abstract

We study the evolution of nonlinear superhorizon perturbations in a universe dominated by a complex scalar field. The analysis is performed adopting the gradient expansion approach, in the constant mean curvature slicing. We derive general solutions valid to second order in the ratio $H^{-1}/L$ for scalar field inhomogeneities of size $L$ subject to an arbitrary canonical potential. We work out explicit solutions for the quadratic and the quartic potentials, and discuss their relevance in setting initial conditions required for the simulations of Primordial Black Hole formation.