Cosmology and Fundamental Physics in the Era of Gravitational-Wave Astronomy

The advent of gravitational-wave (GW) astronomy has presented us with a completely new means for observing the Universe, allowing us to probe its structure and evolution like never before. In this thesis, we explore three distinct but complementary avenues for using GW observations to gain new insights into cosmology and fundamental physics. In chapter 1, we study the astrophysical GW background (AGWB): the cumulative GW signal arising from a large number of compact binary coalescences (CBCs) throughout the Universe. Since these compact binaries reside in galaxies, the AGWB contains anisotropies that trace out the large-scale structure of the cosmic matter distribution. We investigate the angular power spectrum of the AGWB, with the goal of developing predictions that can be confronted with directional AGWB searches. In chapter 2, we calculate the nonlinear GW memory emitted by cusps and kinks on cosmic string loops, which are among the most promising cosmological sources of GWs. We show that, surprisingly, the cusp memory signal diverges for sufficiently large loops, indicating a breakdown in the validity of the weak-field description of the cusp. We then present one tentative possible solution to this divergence, in which the portion of the string surrounding the cusp collapses to form a primordial black hole (PBH). Finally, in chapter 3 we develop a powerful new method for GW detection based on precision measurements of the orbits of binary systems. In the presence of a stochastic GW background (GWB) the trajectories of the binary's components are perturbed, giving rise to a random walk in the system's orbital parameters over time. We calculate the sensitivity of binary pulsars and lunar laser ranging to the GWB through this effect, and show that present data are already sensitive enough to place the strongest constraints to date in the $\mu$Hz frequency band.