Representação escalar-tensorial em gravitação modificada

Abstract

The need to consider quantum effects and the presence of singularities in the solutions of general relativity indicate the desire necessary to study different models of modified gravity. In addition there is a hope of using these models to better understand the accelerationoftheUniverse.Itiswellknownthatthesetypesoftheoriescanbeequivalent to the metric-scalar models with different mechanisms of equivalence. The main goal of ourworkistosuggestamodificationandgeneralizationoftheseknownmechanismsthat can be applied to a wide variety of gravitational theories. In the first part we use functions f(R) for the Friedmann-Lemaître-Robertson-Walker equations and calculate the many solutions of exponential type. Then, we propose a generalization of this theory for functions of type f(Xi), where Xi can be R, R, GaussBonnet, the square of the Weyl tensor and so on. Finally we analyze the future prospects of these models of modified gravity. In the second part of this thesis is a brief introduction to the f(R) theory and suggest a scalar-tensor representation equivalent to this theory. Then, we calculate the gravitational field equations by the direct method using the scalar-tensor action and varying with respect to the spherically symmetric metric. Soon after we find the same field equations, but using the method of conformal transformation. Finally we see the prospects for continuing this work, still in the process and conclusion.