# Perturbations in higher derivative gravity beyond maximally symmetric spacetimes

## TL;DR

This paper investigates scalar-vector-tensor perturbations in infinite derivative gravity around non-maximally symmetric backgrounds, revealing mode coupling and conditions for ghost-free solutions, with implications for non-singular cosmology and black hole physics.

## Contribution

It extends previous perturbation analyses to more general backgrounds, showing mode coupling and identifying conditions for ghost-free solutions in higher derivative gravity.

## Key findings

- All SVT modes are generally coupled at quadratic order.
- Diagonalization of the action can yield ghost-free solutions.
- Results are applicable to non-singular cosmology and black hole models.

## Abstract

We study (covariant) scalar-vector-tensor (SVT) perturbations of infinite derivative gravity (IDG), at the quadratic level of the action, around conformally-flat, covariantly constant curvature backgrounds which are not maximally symmetric spacetimes (MSS). This extends a previous analysis of perturbations done around MSS, which were shown to be ghost-free. We motivate our choice of backgrounds which arise as solutions of IDG in the UV, avoiding big bang and black hole singularities. Contrary to MSS, in this paper we show that, generically, all SVT modes are coupled to each other at the quadratic level of the action. We consider simple examples of the full IDG action, and illustrate this mixing and also a case where the action can be diagonalized and ghost-free solutions constructed. Our study is widely applicable for both non-singular cosmology and black hole physics where backgrounds depart from MSS. In appendices, we provide SVT perturbations around conformally-flat and arbitrary backgrounds which can serve as a compendium of useful results when studying SVT perturbations of various higher derivative gravity models.