Geometrical Trinity of Unimodular Gravity

TL;DR

This paper develops a Weyl transverse diffeomorphism invariant teleparallel gravity theory, equivalent to unimodular gravity and Einstein's general relativity, offering three alternative formulations with a consistent spin-two graviton.

Contribution

It introduces a novel Weyl invariant teleparallel gravity framework that reproduces unimodular gravity and Einstein's GR, expanding the theoretical landscape with multiple equivalent formulations.

Findings

Equivalent to unimodular gravity and Einstein's GR at the non-linear level

Constructs a Weyl invariant teleparallel gravity theory

Provides three alternative formulations of unimodular gravity

Abstract

We construct a Weyl transverse diffeomorphism invariant theory of teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to unimodular gravity (as well as Einstein's general relativity with an adjustable cosmological constant) at the non-linear level. Combined with our earlier construction of a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity, unimodular gravity is represented in three alternative ways.