Removing Ostrogradski's ghost from cosmological perturbations in $f(R,R_{\mu\nu}^2,C_{\mu\nu\rho\sigma}^2)$ gravity

TL;DR

This paper demonstrates that adding constraints to $f(R,R_{},C_{})$ gravity theories effectively removes Ostrogradski's ghost from cosmological perturbations and derives the primordial tensor spectrum.

Contribution

It extends the stabilization method for higher-derivative gravity theories to cosmological backgrounds and provides a formula for the primordial tensor spectrum.

Findings

Ostrogradski's ghost can be removed in cosmological $f(R,R_{},C_{})$ theories.

The stabilization scheme works on generic cosmological backgrounds.

A general formula for the primordial tensor spectrum is derived.

Abstract

Recently it was argued that gravity with the squire of the Ricci tensor can be stabilized by adding constraints to the theory. This was so far demonstrated for fluctuations on the Minkowski/de Sitter background. We show that the same scheme works equally well for removing Ostrogradski's ghost from fluctuations on a cosmological background in generic $f(R,R_{\mu\nu}^2,C_{\mu\nu\rho\sigma}^2)$-type theories of gravity. We also derive the general formula for the spectrum of primordial tensor perturbations from the stabilized theory.