# A gauge invariant prescription to avoid $\gamma$-crossing instability in Galileon bounce

## TL;DR

This paper presents a gauge-invariant method to stabilize the evolution of scalar perturbations across the $ ext{ extgamma}$-crossing point in non-singular Galileon bounce models, avoiding numerical instabilities.

## Contribution

It introduces a gauge-invariant approach to handle $ ext{ extgamma}$-crossing, enabling stable evolution of perturbations without gauge choice ambiguities.

## Key findings

- Perturbations can be evolved across $ ext{ extgamma}$-crossing without instabilities.
- The method is demonstrated in a matter bounce scenario with Galileon action.
- Provides a stable numerical framework for Galileon bounce perturbations.

## Abstract

We revisit the evolutions of scalar perturbations in a non-singular Galileon bounce. It is known that the second order differential equation governing the perturbations is numerically unstable at a point called $\gamma$-crossing. This instability is usually circumvented using certain gauge choices. We show that the perturbations can be evolved across this point by solving the first order differential equations governing suitable gauge invariant quantities without any instabilities. We demonstrate this method in a matter bounce scenario described by the Galileon action.