Generalized unimodular gravity as a form of k-essence

TL;DR

This paper shows that generalized unimodular gravity can be reformulated as a specific k-essence theory, providing a covariant framework and connecting it to effective field theories and self-gravitating media models.

Contribution

It introduces a covariant reformulation of generalized unimodular gravity as a particular k-essence model, clarifying its dynamics and relation to other theories.

Findings

GUMG is dynamically equivalent to a specific k-essence theory.

Three of four Stueckelberg fields decouple in GUMG.

Explicit reconstruction of the k-essence Lagrangian from GUMG parameters.

Abstract

We consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations. Such class of modified gravity models includes recently suggested generalized unimodular gravity (GUMG) theory and its simplest version -- unimodular gravity (UMG). We make these gravity models covariant by introducing four Stueckelberg fields and show that in the case of generalized unimodular gravity three out of these fields dynamically decouple. This means that the covariant form of generalized unimodular gravity is dynamically equivalent to k-essence theory with a specific Lagrangian which can be reconstructed from the parameters of GUMG theory. We provide the examples, where such reconstruction can be done explicitly, and briefly discuss theories beyond GUMG, related to self-gravitating media models. Also we compare GUMG k-inflation with cuscuton models of dynamically inert k-essence field and discuss motivation for GUMG coming from effective field theory.