Probing the Dark Universe with Gravitational Waves

Abstract

Gravitational wave (GW) astronomy opens new opportunities to explore the universe and its fundamental laws. This thesis focuses on probing the pillars of the standard cosmological model with GWs, specially its most puzzling components: dark energy (DE) and dark matter (DM). We propose and apply new tests of DE and General Relativity (GR) with the propagation of GWs. We also investigate the formation of black-holes (BHs) in the early universe, which has strong implications on their contribution to the DM and on their GW signatures. Just as electromagnetic radiation can scan materials, GWs can probe the medium in which they propagate. DE models beyond Einstein’s gravity generically modify the propagation of GWs. We identify the speed of GWs as a key test of gravity and find the conditions for an anomalous speed to arise. We emphasis that a non-luminal speed can appear in cosmological models aiming at DE such as Galileons, but also in environments with a spatial profile induced by screening or scalar hair. After the multi-messenger event GW170817, we determine the consequences of the tight constraint on the speed of GWs for different classes of gravity theories and DE models, setting the dead ends and the road ahead. Standard sirens like GW170817 constrain as well the GW luminosity distance. We derive this observable in general theories of gravity and discuss its detectability with the future space-based detector LISA. Particularly distinguishable oscillatory patters are produced by GW oscillations, a phenomenon that we study in detail. Other probes of GW oscillations are modified wave-forms, induced anomalous speeds and polarization dependent signals. Primordial BHs (PBHs) could be a unique relic to unveil the physics of the early universe. We study the production of PBHs in single field model of inflation with a quasi-inflection point, showing the growth of perturbations beyond slow-roll (SR) at sub- and super-horizon scales. We propose a particle physics motivated model, critical Higgs inflation, achieving a copious PBH production with several GW signatures. However, when curvature fluctuations are enhanced, quantum diffusion dominates the classical inflationary dynamics. We develop a formalism based on stochastic inflation beyond SR to account for this effect. We encounter that the classical prediction is importantly modified, with relevant non-Gaussian contributions. To quantify better the quantum correction, we devise a method to compute directly the tail of the curvature perturbation distributions. As a first step, we apply it to SR inflation. We conclude that the abundance of PBHs is many orders of magnitude larger than the Gaussian prediction, discussing its implications for inflationary model building as well as for the GW observables. Altogether, GW astronomy stands as a powerful channel to advance forward in the quest for understanding the dark universe. We discuss the future prospects of this line of research, highlighting the theoretical challenges and observational opportunities that next generation GW detectors will provide.