On cosmological perturbations in FRW model with scalar field and false vacuum decay

TL;DR

This paper derives a reduced action for scalar fluctuations in FRW cosmology with gravity, clarifies the negative mode problem in false vacuum decay, and demonstrates the existence of negative modes in certain models.

Contribution

It provides a new derivation of the reduced action using Dirac's method, clarifies the negative mode issue, and shows the consistency with existing theorems.

Findings

Existence of negative modes in false vacuum decay scenarios.

A special choice of variables yields a conventional kinetic term signature.

The results align with the no negative mode theorem.

Abstract

The unconstrained reduced action corresponding to the dynamics of scalar fluctuations about the Friedmann-Robertson-Walker (FRW) background is derived using Dirac's method of description of singular Lagrangian systems. The results are applied to so-called negative mode problem in description of tunneling transitions with gravity. With our special choice of physical variable, the kinetic term of the reduced action has a conventional signature for a wide class of models. In this representation, the existence of a negative mode justifying the false vacuum decay picture turns out to be manifest. We also explain how the present result becomes consistent with the previously proved ``no negative mode (supercritical supercurvature mode) theorem''.