A Dinâmica Cosmológica na gravidade f(R,T) - Dias, Ana Paula Jeakel (2023)
We begin with a comprehensive analysis of the key concepts in General Relativity and Cosmology, thus laying a strong foundation that will enable a thorough understanding of the central topic addressed in this research. Subsequently, we delve into the core of this study, where we conduct a detailed review of the current state of f(R; T) theories, where T represents the trace of the energy-momentum tensor Tμν, concerning the evolution of the cosmological background expansion of Friedmann-Lemaître-Robertson-Walker (FLRW). We start focusing on the modified Friedmann equations for the case of a minimally coupled gravitational Lagrangian of the type f(R; T) = R+ αeβΤ + γnTn. With this choice one covers all existing proposals in the literature via four free parameters. All relevant f(R; T) models as well as the CDM model can be achieved in the appropriate limit. We show that in such a minimally coupled case there exists a useful constraining relation between the effective total matter density with an arbitrary equation of state parameter and the modified gravity parameters. Then, with this association the modified gravity sector can be independently constrained using estimations of the gas mass fraction in galaxy clusters. Further, using cosmological background cosmic chronometers data and demanding the universe is old enough to accommodate the existence of Galactic globular clusters with estimated age of at least ~ 14 Gyrs we find a narrow range of the modified gravity free parameter space in which this class of theories remains viable for the late time cosmological evolution. As expected, this preferred parameter space region accommodates the CDM limit of f(R; T) models. However, when analysing the cosmological dynamics including a radiation component, we find that this energy density interacts with the matter field and it does not scale according to the typical a-4 behavior, being a the scale factor. We conclude stating that f(R; T) gravity is not able to provide a full cosmological scenario and should be ruled out as a modified gravity alternative to the dark energy phenomena.