Solutions of gauge invariant cosmological perturbations in long-wavelength limit

TL;DR

This paper presents a method to derive gauge invariant solutions for cosmological perturbations in a flat universe with scalar fields, especially useful in the long-wavelength limit and for multiple scalar fields.

Contribution

It introduces a technique to obtain gauge invariant solutions by differentiating background solutions with respect to parameters, simplifying analysis of long-wavelength perturbations.

Findings

Solutions can be derived by parameter differentiation of background solutions.

Method is effective for multiple scalar fields.

Provides exact solutions in the long-wavelength limit.

Abstract

We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the long-wavelength limit. We find that these gauge invariant solutions can be obtained by differentiating the background solution with respect to parameters contained in the background system. This method is very useful when we analyze the long-wavelength behavior of cosmological perturbation with multiple scalar fields.