Einsteinian cubic gravity

TL;DR

This paper introduces a simplified method for linearizing higher-order gravity theories and constructs a unique cubic gravity theory in D dimensions that shares Einstein gravity's spectrum and is non-trivial in four dimensions.

Contribution

It develops a new approach to linearize higher-order gravity theories and identifies a unique cubic gravity theory satisfying key physical properties across dimensions.

Findings

Constructed a D-dimensional cubic gravity theory with Einstein spectrum

Identified a unique non-trivial cubic theory in four dimensions

Demonstrated the theory's invariance of curvature coefficients across dimensions

Abstract

We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect to one of those parameters. We use our method to construct a D-dimensional cubic theory of gravity which satisfies the following properties: 1) it shares the spectrum of Einstein gravity, i.e., it only propagates a transverse and massless graviton on a maximally symmetric background; 2) the relative coefficients of the different curvature invariants involved are the same in all dimensions; 3) it is neither trivial nor topological in four dimensions. Up to cubic order in curvature, the only previously known theories satisfying the first two requirements are the Lovelock ones: Einstein gravity, Gauss-Bonnet and cubic-Lovelock. Of course, the last two theories fail to satisfy requirement 3 as they are, respectively, topological and trivial in four dimensions. We show that, up to cubic order, there exists only one additional theory satisfying requirements 1 and 2. Interestingly, this theory is, along with Einstein gravity, the only theory which also satisfies 3.