Abordagem não-conservativa da teoria unimodular:aplicação a cenários cosmológicos
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Data
2025-03-21
Autores
Alvarenga, Marcelo Henrique de
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Universidade Federal do Espírito Santo
Resumo
The unimodular theory is one of the simplest modification of the theory of General Relativity (GR). According to the set of symmetries present in Unimodular Gravity (UG), it is invariant to a subclass of diffeomorphism transformations, transverse diffeomorphism (Tdiff), which pre serves the determinant of the metric tensor. This characteristic leads to the field equations in GU being trace-free. A direct consequence, which differs from GR, is that the Bianchi identities no longer lead directly to the conservation of the energy-momentum tensor, that is, the general law of conservation is an imposition made separately on the structure of the field equations in UG. In fact, if the imposition is made, the resulting equations are GR+Λ, however, the cosmological constant appears as an integration constant. This fact leads to many discussions about the equivalence between theories. In this work we explore the issue of imposing the conservation of the energy-momentum tensor as a necessary condition to recover the equivalence between UG and GR+Λ. Conservation law is a matter of choice and we chose to maintain the nonconserva tive nature. We study the consequences of this non-imposition in cosmological scenarios. We explore cosmological evolution and show that there is a viable cosmological model that transi tions from a radiative phase to an accelerated de Sitter-type expansion. Furthermore, we also analyze cosmological perturbations in non-conservative Unimodular Gravity (NUG). We show that, unlike the usual unimodular theory, in NUG we can use the synchronous gauge condition and analyze both scalar and tensor modes. This leads to interesting signatures that differ from RG. We also study scalar perturbations in the gauge invariant formalism; in vacuum solutions and by imposing the conservation of the energy-momentum tensor, we recover the same equations as in GR. But, when we add matter fields, the equations are different and we end up in an underdetermined system. We also propose a study within the cosmological context in NUG considering the dark energy component as holographic, which led us to construct a viable back ground cosmological model. According to the analysis of cosmological perturbations in both cases, the equivalence between UG and GR seems to be incomplete.
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Palavras-chave
Relatividade geral , Gravidade unimodular , Modelo cosmológico padrão , Princípio holográfico