Born-Infeld Gravity with a Massless Graviton in Four Dimensions

TL;DR

This paper develops Born-Infeld gravity theories in four dimensions that ensure unitarity and a massless graviton, addressing challenges in constructing such theories around (anti)-de Sitter backgrounds.

Contribution

It introduces a perturbative method to construct unitary Born-Infeld gravity theories in four dimensions, including the role of Gauss-Bonnet terms in the process.

Findings

Successfully constructed BI theories with massless gravitons in 4D

Identified the importance of Gauss-Bonnet terms in theory viability

Provided a perturbative framework for BI gravity around (A)dS backgrounds

Abstract

We construct Born-Infeld (BI) type gravity theories which describe tree-level unitary (non-ghost and non-tachyonic) massless spin-2 modes around their maximally symmetric vacua in four dimensions. Building unitary BI actions around flat vacuum is straightforward; but, this is a complicated task around (anti)-de Sitter backgrounds. In this work, we solve the issue and give details of constructing perturbatively viable determinantal BI theories. It is interesting that the Gauss-Bonnet combination, which is a total derivative in four dimensions, plays an important role in the construction of viable BI theories.