Geometrical trinity 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.

Tidal Deformability of Neutron Stars in Unimodular Gravity

“…Substituting (20) into the left hand side of Equation ( 6) and keeping only up to the first order terms in h µν , one reaches the linearized UG equations…”

“…UG with or without the hypothesis of conservation of the energy-momentum tensor has been extensively investigated in the literature [17][18][19][20][21], particularly in the context of cosmology [22][23][24][25][26] and in the quantization problem of gravity [27][28][29]. Recently, the evolution of gravitational waves in UG without the conservation of the energy-momentum tensor is considered, and the differernce compared to the usual signatures in GR is shown [30].…”

General parallel cosmology

“…[3,4, for their cosmological applications. The complementary descriptions of the gravitational interaction provided by those two alternatives in conjunction with the conventional one form the so called geometrical trinity of gravity [51], which has been discussed from various different perspectives in the recent literature [52][53][54][55][56][57][58][59][60][61][62]. The version of GR in the generalised framework interpolating the base of the geometrical trinity of gravity was called "the general teleparallel equivalent of general relativity" [22], but since the relativistic theory we consider here is not an equivalent to GR, 1 we refer to it more briefly as G ∥ R.…”