Invariant dynamics of scalar perturbations of inflanton and gravitational fields

TL;DR

This paper develops a gauge-independent invariant theory for scalar perturbations in inflation and gravitational fields, enabling unambiguous analysis of physical effects and correcting overestimations caused by common gauges.

Contribution

It introduces a new invariant framework for analyzing scalar perturbations in inflation, clarifying gauge issues and improving the accuracy of back reaction and quantum fluctuation studies.

Findings

The invariant theory corrects overestimations from longitudinal gauge.

It confirms the Lifshitz gauge's suitability for inflation analysis.

The theory applies to quantum fluctuations and stability of inflation.

Abstract

A gauge-independent, invariant theory of linear scalar perturbations of inflation and gravitational fields has been created. This invariant theory allows one to compare gauges used in the work of other researchers and to find the unambiguous criteria to separate the physical and coordinate effects. It is shown, in particular, that the so-called longitudial gauge, commonly used when considering inflation instability, leads to a fundamental overestimation of the effect because of non-physical perturbations of the proper time in the frame of reference specified by this gauge. Back reaction theories employing this sort of gauge [1] also involve coordinate effects. The invariant theory created here shows that the classical Lifshitz (1946) [2] gauge does not lead to non-physical perturbations of the proper time and can be used to analyze the inflation regime and the back reaction of perturbations on this regime properly. The first theory of back reaction on background of all types of perturbations (scalar, vector and tensor) based on this gauge was published in 1975 [3] and has been applied recently to the inflation [4]. The investigation of long-length perturbations, which characterize the stability of the inflationary process, and quantum fluctuations, which form the Harrison-Zel'dovich spectrum at the end of inflation, is performed in the invariant form. The invariant theory proposed allows one to examine the effect of quantum fluctuations on the inflationary stage when the periodic regime changes to an aperiodic one. That only the invariant theory must be used to analyze space experiments is one of the conclusions of the present work.