Regular Article - Theoretical Physics
Nonconservative unimodular gravity: a viable cosmological scenario?
Núcleo Cosmo-ufes and Departamento de Física, Universidade Federal do Espírito Santo (UFES), Av. Fernando Ferrari, 540, CEP 29.075-910, Vitória, ES, Brazil
2 National Research Nuclear University MEPhI, Kashirskoe sh. 31, 115409, Moscow, Russia
3 Département de Physique, Université de Niamey, Niamey, Niger
4 Departamento de Física, Universidade Federal de Ouro Preto (UFOP), Campus Universitário Morro do Cruzeiro, 35.400-000, Ouro Prêto, Brazil
Accepted: 24 May 2022
Published online: 11 June 2022
In this work we review the issue of imposing the conservation of the energy–momentum tensor as a necessary condition to recover the equivalence between the unimodular gravity and General Relativity (GR) equipped with a cosmological constant. This procedure is usually interpreted as an ad hoc imposition on the unimodular theory’s structure. Whereas the consequences of avoiding the conservation of the total energy–momentum tensor has been already introduced in the literature, it has been not widely explored so far. We study an expanding universe sourced by a single effective perfect fluid such that the null divergence of its energy–momentum tensor is not imposed. As we shall show, in this scheme, the unimodular theory has its own conservation equation obtained from the Bianchi identities. We explore the evolution of the homogeneous and isotropic expanding background and show that a viable cosmological scenario exists. Also, we consider scalar perturbations with particular attention given to the gauge issue. We show that contrary to the traditional unimodular theory where the synchronous and longitudinal (newtonian) gauge for cosmological perturbations are not permitted, if the conservation of the energy–momentum is relaxed the scalar perturbations in the synchronous condition survive and present a growing mode behavior. We study therefore a new cosmological scenario in which the dynamics of the universe transits from the radiative phase directly to a accelerated one but allowing thus for structure formation.
© The Author(s) 2022
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