Cosmological gravitational waves in the limit of geometric optics

Detecting gravitational waves (GWs) propagating through cosmic structures can provide valuable information about the geometry and contents of our Universe, opening a completely new window for observational astrophysics. In order to carry out astrophysical and cosmological studies it is important to have a precise formalism for using GW observations. In this thesis we will consider GWs traveling through a perturbed FRW background and work with the geometric optics approximation. In particular, by observing the effect of cosmological perturbations on the GW waveform associated with a merging binary system, we calculate the correction due to the tensor contribution when estimating the luminosity distance anisotropies. Specifically, we compute the signatures left on the GW signal by primordial GWs and analytically derive their signature on the angular power spectrum associated with the relative correction to the luminosity distance.