Non-uniqueness of massless transverse-traceless graviton

TL;DR

This paper investigates a modified gravity theory called cuscuton/VCDM, demonstrating that it fundamentally differs from general relativity even in vacuum, challenging the idea that it could be a simple field redefinition of GR.

Contribution

It proves that the cuscuton/VCDM theory cannot be obtained from GR via a field redefinition, establishing its distinctness in vacuum.

Findings

The theory propagates only two gravitational degrees of freedom.

A field redefinition from GR to this theory does not exist.

The theory differs from GR in vacuum, not just with matter.

Abstract

We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist and that the theory differs from GR already in vacuum.