Vorticity and Gravitational Wave Perturbations on Cosmological Backgrounds Using the 1+1+2 Covariant Split of Spacetime

Abstract: In this thesis we consider perturbations of a perfect fluid on locally rotationally symmetrical (LRS) class II cosmological backgrounds, with a nonvanishing vorticity of the fluid on the perturbed model. The method used is based on the 1+1+2 covariant decomposition of spacetime, motivated by the assumption of anisotropic expansion, followed by a harmonic decomposition of all gauge invariant quantities. All perturbed quantities can be solved for in terms of the time evolution equations of eight harmonic coefficients. This set of eight harmonic coefficients decouple into an even and odd sector, containing five and three variables respectively, where the vorticity is represented as one variable in each sector. We find that the time evolution of the vorticity completely decouples from the other perturbed variables, and can be solved exactly by assuming a linear equation of state. The evolution of the remaining perturbed variables are examined in the geometrical optics approximation, and compared to research looking at the case when the vorticity vanishes on the perturbed model. The results turn out to be the same, except for a source term containing the odd parity of the vorticity in the evolution of the density, which act as a source term for the shear waves. The four remaining variables will represent damped, source free gravitational waves.