Ripples from the Early Universe to the Present

In this thesis we study a range of topics in cosmology and gravitational wave physics, emphasizing their roles as probes of fundamental physics across vastly different scales. On the cosmology side, we focus on the analysis of the bispectrum, which provides unique insights into the physics of the early universe. Our work includes a calculation of the bispectrum in the squeezed-limit in quasi-single field inflation using Conformal Fermi Coordinates, a demonstration of the equivalence of different regularization prescriptions for the galaxy bias expansion, and the first numerical evaluation of the bispectrum in the Spherical Fourier-Bessel basis. On the gravitational wave side, we present an analytical template for the ring-down signal from rotating exotic compact objects, with applications to searches in interferometer data.