Efeitos de termos de ordem superior e acoplamentos não-mínimos sobre a gravitação de Einstein-Hilbert

Abstract

This master thesis has the goal to revise some aspects of the Einstein's gravitation, focused on techniques of compute the graviton's Feynman propagator in Einstein-Hilbert theory and mo di ed models of gravity. For this purpose, we show the tensorial projectors formalism suitable for the gravitational eld case (spin-2 eld) in the famous Barnes-Rivers basis. We emphasize that for each gravity model considered exist a distinct set of operators that form a closed alge bra, and that the formalism of tensorial projectors only work when we consider the suitable set for each speci c case. Such formalism, besides being very elegant, is quite powerful because it allows calculating the graviton's propagator in di erent gravitational theories. In possession of the propagator, we obtain the dispersion relations, which allow access to information related to the propagation of signals and about the excitations of the theory. In this work, we review the algorithm to compute the graviton's propagator in four di erent theories. The rst of these is the non-massive Einstein-Hilbert gravitation, where we consider the Lagrangian density only composed by the Ricci scalar (R). The second one consists of an extended version of the Einstein-Hilbert gravitational theory, modi ed by quadratic terms, that is, in addition to the Ricci scalar, the Lagrangian of this model has terms of the type R2 and RµνRµν. The third is the gravitation of Einstein-Chern-Simons, which is a theory for gravity in (2 + 1) dimensions. In this model, the operators that compose the Barnes-Rivers basis do not form a closed set, requiring an extended version to obtain the propagator. Finally, we approach a theory of gra vitation constituted by the coupling between the bumblebee eld (bµ) and the Einstein-Hilbert lagrangian. An extension of the Barnes-Rivers basis is also necessary here, through the projec tors that contain the bumblebee eld, which is the violator of Lorentz's symmetry.