Cosmological wave asymptotics in the direction of the initial singularity

This thesis looks into systems of linear wave equations on cosmological backgrounds. The main aim is to investigate the asymptotics of solutions to such equations, particularly in the direction of the initial singularity of these background models. As an application, the past asymptotics of two linear wave equations on a flat Friedmann-Lemaˆıtre solution, coupled to a perfect fluid, are analyzed. The first equation describes linear scalar perturbations of such a background in the presence of a cosmological constant Λ. Of interest is the effect Λ could have on the asymptotics of these perturbations. The second equation, on the other hand, represents the equation of motion of a massive scalar field on the same background. In this respect, the asymptotic expansion, and hence the blow-up profile, of the relevant physical quantities is derived and compared with previous results.