Nonconservative unimodular gravity : a viable cosmological scenario?

Abstract

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 unimod- ular 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 struc- ture. Whereas the consequences of avoiding the conserva- tion 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 sin- gle 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 cosmologi- cal 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 cosmo- logical 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 sce- nario in which the dynamics of the universe transits from the

radiative phase directly to a accelerated one but allowing thus for structure formation.