Towards construction of ghost-free higher derivative gravity from bigravity

TL;DR

This paper rigorously proves the ghost-free nature of a higher derivative gravity theory derived from bigravity, extending previous linear approximations to a full non-perturbative analysis.

Contribution

It demonstrates the elimination of ghosts in a higher derivative gravity model without relying on linear approximations, using a comprehensive non-perturbative approach.

Findings

Ghosts can be eliminated in the model with arbitrary nonderivative interactions.

The analysis extends beyond linear approximation to all orders.

The model remains consistent and ghost-free in a full non-perturbative framework.

Abstract

In this paper, the ghost-freeness of the higher derivative theory proposed by Hassan et al. in [Universe 1 (2015) 2, 92] is investigated. Hassan et al. believed the ghost-freeness of the higher derivative theory based on the analysis in the linear approximation. However, in order to obtain the complete correspondence, we have to analyze the model without any approximations. In this paper, we analyze two scalar model proposed in [Universe 1 (2015) 2, 92] with arbitrary nonderivative interaction terms. In any order with respect to perturbative parameter, we prove that we can eliminate the ghost for the model with any nonderivative interaction terms.