Perturbative analysis of generalized Einstein's theories
J.C. Fabris (1), R. Kerner (2), J. Tossa (3) ((1) Departamento de, Fisica, Universidade Federal do Espirito Santo, (2) Laboratoire de, Gravitation et Cosmologie Relativistes, Universite Pierre et Marie Curie, (3), IMSP, Universite du Benin)

TL;DR
This paper performs a perturbative analysis of generalized Einstein's theories where matter energy-momentum is not conserved, exploring their implications for cosmic evolution and gravitational phenomena, identifying a promising theory among two considered.
Contribution
It introduces a perturbative approach to analyze two generalized Einstein's theories, providing analytical solutions for cosmological perturbations and assessing their physical viability.
Findings
One theory shows satisfactory cosmological properties.
The other theory is inconsistent and should be discarded.
Analytical expressions for gravitational wave and density evolution are derived.
Abstract
The hypothesis that the energy-momentum tensor of ordinary matter is not conserved separately, leads to a non-adiabatic expansion and, in many cases, to an Universe older than usual. This may provide a solution for the entropy and age problems of the Standard Cosmological Model. We consider two different theories of this type, and we perform a perturbative analysis, leading to analytical expressions for the evolution of gravitational waves, rotational modes and density perturbations. One of these theories exhibits satisfactory properties at this level, while the other one should be discarded.
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