Manifestly gauge invariant theory of the nonlinear cosmological perturbations in the leading order of the gradient expansion

TL;DR

This paper develops a gauge-invariant framework for nonlinear cosmological perturbations, defining variables and conditions in a way that simplifies analysis of the evolution and non-Gaussianity in the early universe.

Contribution

It introduces a fully gauge-invariant formulation of nonlinear perturbation theory and provides methods to estimate non-Gaussianity, especially from entropic perturbations.

Findings

All physical laws can be expressed using gauge-invariant variables.

The nonlinear parameter $f_{NL}$ can be estimated analytically.

Significant non-Gaussianity requires a very small entropic scalar field.

Abstract

In the full nonlinear cosmological perturbation theory in the leading order of the gradient expansion, all the types of the gauge invariant perturbation variables are defined. The metric junction conditions across the spacelike transition hypersurface are formulated in a manifestly gauge invariant manner. It is manifestly shown that all the physical laws such as the evolution equations, the constraint equations, and the junction conditions can be written using the gauge invariant variables which we defined only. Based on the existence of the universal adiabatic growing mode in the nonlinear perturbation theory and the $\rho$ philosophy where the physical evolution are described using the energy density $\rho$ as the evolution parameter, we give the definitions of the adiabatic perturbation variable and the entropic perturbation variables in the full nonlinear perturbation theory. In order to give the analytic order estimate of the nonlinear parameter $f_{NL}$, we present the exponent evaluation method. As the models where $f_{NL}$ changes continuously and becomes large, using the $\rho$ philosophy, we investigate the non-Gaussianity induced by the entropic perturbation of the component which does not govern the cosmic energy density, and we show that in order to obtain the significant non-Gaussianity it is necessary that the scalar field which supports the entropic perturbation is extremely small compared with the scalar field which supports the adiabatic perturbation.