Ghost-free higher order gravity from bi-gravity

TL;DR

This paper derives a ghost-free higher order gravity model from Hassan-Rosen bi-gravity by recursive metric absorption, extending to fourth order and discussing its effective, infinite-derivative limit with implications for perturbative validity.

Contribution

It introduces a novel recursive approach to obtain ghost-free higher order gravity from bi-gravity, extending previous conformal gravity results to fourth order and beyond.

Findings

Derived fourth order gravity model from bi-gravity

Identified the effective infinite-derivative limit for ghost-free gravity

Showed graviton mass influences the perturbative regime

Abstract

In this work we studied the higher order gravity model which corresponds to Hassan-Rosen ghost-free bi-gravity. To do this we absorb one of the metrics in bi-gravity model in favor of the other metric in a recursive way. For the second (recursion) step we get conformal gravity same as what has been done in the literature. We generalize this idea by calculating up to the fourth order gravity. To reach to a ghost-free higher order gravity we need to go to infinite-derivative order gravity but we can see our model as an effective theory. So adding higher order terms results in wider range of validity of our model. We emphasize that graviton mass controls the validity of perturbative approach.