# Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric

## TL;DR

This paper investigates the stability of higher derivative gravity with Bianchi-I metrics, confirming that linear stability extends to the nonperturbative level for small anisotropies, supporting the robustness of previous linear analyses.

## Contribution

It provides a comparison between linear and nonperturbative stability solutions in higher derivative gravity with Bianchi-I metrics, validating the linear stability results.

## Key findings

- Linear stability aligns with nonperturbative asymptotic behavior.
- Small anisotropies do not lead to ghost instabilities.
- Linear analysis is reliable for certain gravitational perturbations.

## Abstract

The study of stability of gravitational perturbations in higher derivative gravity has shown that at the linear level the massive unphysical ghost is not generated from vacuum if the initial seed of metric perturbation has frequency essentially below the Planck threshold. The mathematical knowledge indicated that the linear stability is supposed to hold even at the nonperturbative level, but in such a complicated case it is important to perform a verification of this statement. We compare the asymptotic stability solutions at the linear and full nonperturbative levels for the Bianchi-I metric with small anisotropies, which can be regarded as an extreme, zero frequency limit of a gravitational wave. As one should expect from the combination of previous analysis and general mathematical theorems, there is a good correspondence between linear stability and the nonperturbative asymptotic behavior.