Probing cosmological growth and expansion with the peculiar velocity field

This thesis studies how the velocities of galaxies in the nearby Universe can be used to make optimal measurements of the current expansion rate of the Universe and to accurately measure how structure grows in the Universe, under the influence of gravity. To do so, this thesis develops novel methods of measuring the cross-correlation between the peculiar velocities of galaxies and their positions in the sky, reducing the measurement error in key cosmological parameters. Different models of gravity will predict different behaviours in the rates of expansion and growth, this thesis provides an avenue for exploring these alternative theories.