Perturbation initial conditions for a couple of dark energy scalar field potentials

TL;DR

This paper derives initial perturbation conditions for two common dark energy scalar field potentials, considering different gauge choices and fluid components, aiding accurate cosmological modeling.

Contribution

It introduces a method to derive initial conditions for scalar field perturbations in multiple gauge settings, applicable to various dark energy models.

Findings

Provides explicit initial conditions for inverse power-law and exponential potentials.

Demonstrates gauge transformation technique for deriving solutions in different gauges.

Enhances precision in cosmological simulations involving dark energy scalar fields.

Abstract

We present perturbation initial conditions for two types of scalar field potential often used in the dark energy study: one inverse power-law and the other exponential. The solutions are presented in the presence of the $w =$ constant fluid ($w = 1/3$ for radiation fluid), a minimally coupled scalar field and a sub-dominating zero-pressure fluid (cold dark matter and baryon dust). We consider two gauge conditions, the $w$-fluid comoving gauge and the cold-dark-matter comoving gauge; solutions in the latter gauge are derived by the gauge transformation and this method can be applied to derive solutions in any other gauge condition.