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 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.
