Beyond Lovelock gravity: Higher derivative metric theories

TL;DR

This paper explores higher derivative metric theories of gravity in four dimensions, identifying degenerate Lagrangians beyond Einstein-Hilbert, including Chern-Simons and new chiral scalar-tensor theories, with implications for stability and effective field descriptions.

Contribution

It classifies degenerate higher derivative gravity theories, introduces new chiral scalar-tensor models, and analyzes their stability and physical relevance.

Findings

Identified a set of degenerate Lagrangians beyond Einstein-Hilbert.

Revealed potential instabilities in Chern-Simons gravity.

Proposed new parity-violating chiral scalar-tensor theories.

Abstract

We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than two degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories". Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.