Perturbations in higher derivative gravity beyond maximally symmetric spacetimes

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 that 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 that 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 we illustrate this mixing and also a case where the action can be diagonalized and a ghost-free spectrum constructed. Our study is widely applicable for both nonsingular cosmology and black hole physics where backgrounds depart from MSS. In the appendixes, we provide SVT perturbations around conformally flat and arbitrary backgrounds which can serve as a compendium of useful results when studying various higher derivative gravity models.

Figure 1

Venn diagram with our specific conformally flat, nonmaximally symmetric background. ${\partial }_{\mu }\overline{R}=0$ follows from ${\overline{\nabla }}_{\alpha }{\overline{S}}_{\mu \nu }=0$. The dS/AdS limit is achieved by putting ${\overline{S}}_{\mu \nu }=0$.