Nonconservative Unimodular Gravity: Gravitational Waves

Marcelo H Alvarenga,Mahamadou Hamani Daouda,Hermano Velten,Júlio C Fabris

doi:10.3390/sym14010087

Marcelo H Alvarenga, Mahamadou Hamani Daouda + Show 2 more

Open Access

https://doi.org/10.3390/sym14010087

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Abstract

Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.

Highlights

Academic Editor: IgnatiosGeneral relativity (GR) is considered as the modern theory of gravitation since its final formulation in 1915
For a detailed discussion on the transverse diffeomorphism, see for example [2] and references therein. The invariance by this restricted class of transformations, with respect to the general diffeomorphism, in the unimodular gravity has one particular consequence for the divergence of the energy–momentum tensor: it can be zero, implying the usual conservation laws and the GR equations are recovered with an extra integration constant, which can be identified with the cosmological constant; or the energy–momentum tensor is Received: 30 November 2021
Unimodular gravity is a theory of gravity almost as old as GR

Summary

Introduction

General relativity (GR) is considered as the modern theory of gravitation since its final formulation in 1915. For a detailed discussion on the transverse diffeomorphism, see for example [2] and references therein The invariance by this restricted class of transformations, with respect to the general diffeomorphism, in the unimodular gravity has one particular consequence for the divergence of the energy–momentum tensor: it can be zero, implying the usual conservation laws and the GR equations are recovered with an extra integration constant, which can be identified with the cosmological constant; or the energy–momentum tensor is Antoniadis. In the present paper we have a very specific goal: to study the evolution of gravitational waves in a cosmological model resulting from the unimodular gravity with non conservation of the energy–momentum tensor.

Unimodular Gravity

A Cosmological Model

Gravitational Waves

Comparing Unimodular Cosmology with the Standard Cosmological Model

Discussion and Conclusions