Efeitos da violação da simetria de Lorentz na polarização de ondas gravitacionais

Abstract

This work aims to solve Einstein equation in a scenario with Lorentz symmetry violation for gravitational waves polarization. It will be commented about standard model extension, spontaneous and explicit violation of a symmetry as well as their consequences. The bumblebee model will be used for the study of Lorentz violation, where the terms that break off the symmetry are included in the lagrangian of the gravitational theory. The Euler-Lagrange equations are used to determine the modified graviton propagator, where we expand the lagrangian up to second order of the perturbed gravitational field. We see that, in this scenario, the dispersion relation of graviton is different of the usual one, where we have a term that selects a preferred direction in the spacetime. Besides that, the graviton still with two degrees of freedom, despite the existence of bumblebee field. Then, the modified wave equation for perturbation field is solved and we compare the polarization states of the gravitational wave solution modified with the usual case. We show that for a bumblebee field being timelike or in the same direction of wave momentum we have no changes in the polarization tensor. But for a bumblebee field being in another diretion we have a modified polarization tensor for the graviton. Besides that, we compute some bounds for the parameter of the bumblebee field by comparing the group velocity here computed with a group velocity of a massive graviton.