Removing spurious degrees of freedom from EFT of gravity

TL;DR

This paper develops a method to remove extraneous degrees of freedom in effective field theories of gravity, resulting in a minimally modified gravity theory that preserves the massless graviton but introduces a preferred frame at short distances.

Contribution

It introduces an action-based procedure to eliminate spurious degrees of freedom in EFT of gravity, leading to a minimally modified gravity theory with specific properties.

Findings

Reduced theory propagates only the massless spin-2 graviton

The resulting theory exhibits a preferred frame at short distances

The approach clarifies the connection between EFT corrections and modified gravity

Abstract

In the effective field theory approach to gravity, the Lagrangian density for general relativity is supplemented by generally covariant terms of higher order in the Riemann tensor and its derivatives. At face value, these terms will result in higher derivative equations of motion and additional degrees of freedom beyond those of general relativity. This is seemingly at odds with the goal of effective field theory which is to encode ultraviolet corrections in terms of existing low energy degrees of freedom. Here we apply an action-based procedure for the removal of spurious degrees of freedom for the case of general relativity supplemented by a term cubic in the Riemann tensor. To the order we work in, the resulting reduced theory takes the form of minimally modified gravity, which is a class of modified gravity theories that propagate just the massless spin-2 graviton, but exhibit a preferred frame at short distances due to a deformation of time diffeomorphisms. Our work suggests that this class of theories can be understood as an effective theory of gravity, capturing effects of unknown ultraviolet physics.