Novel matter coupling in general relativity via canonical transformation

TL;DR

This paper introduces a new method for matter coupling in general relativity using canonical transformations, resulting in a consistent theory with only two gravitational degrees of freedom and potential applications in modified gravity.

Contribution

The authors develop a novel matter coupling approach in GR via canonical transformations that avoids extra modes and modifies the gravitational dynamics.

Findings

The transformed theory remains equivalent to GR in vacuum.

Naive matter coupling introduces an extra mode, causing inconsistency.

A gauge-fixed matter coupling scheme avoids extra modes and alters cosmological dynamics.

Abstract

We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field. We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent. We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity without generating an unwanted extra mode. As a result, the way matter field couples to the gravitational field determines the preferred time direction and the resultant theory has only two gravitational degrees of freedom. We also discuss the cosmological solution and linear perturbations around it, and confirm that their dynamics indeed differ from those in GR. The novel matter coupling can be used for a new framework of modified gravity theories.