Damping of Gravitational Waves in Cosmology Revisited: Beyond the Standard Case

Gravitational waves (GWs) offer a unique window into the early Universe, providing insights into the physics of inflation, the thermal history of the cosmos, and the nature of dark matter. In particular, primordial gravitational waves (PGWs) interact with the cosmological medium as they propagate, and their evolution is sensitive to the background expansion as well as to the presence of anisotropic stress, free-streaming effects, and non-equilibrium processes. This thesis investigates how two alternative dark matter candidates — ultra-light axions (ULAs) and self-interacting dark matter (SIDM) — modify the propagation of PGWs through their imprint on the energy-momentum tensor. A guiding motivation for this thesis comes from the well-established effect of neutrino free- streaming, which produces a characteristic damping and phase shift in the PGW spectrum by sourcing an anisotropic stress once neutrinos decouple. This effect demonstrates how the microphysics of a cosmological species can be imprinted onto GWs through its energy-momentum tensor. Our analysis extends this perspective to alternative dark matter scenarios, asking whether analogous signatures can arise when the dark sector exhibits either significant self-interactions or a delayed onset of oscillations as in the case of ULAs. In this sense, the treatment of SIDM and ULAs presented here can be viewed as natural generalisations of the neutrino case, probing whether similar damping, phase shifts, or step-like features may survive and potentially serve as novel observational windows on dark matter physics. SIDM, characterized by non-negligible elastic scatterings among dark matter particles, mod- ifies the relaxation rate and the transport properties of the dark matter fluid, leading to changes in the viscous response and suppressing the anisotropic stress more efficiently than in the colli- sionless CDM case. By extending kinetic and hydrodynamic treatments to include elastic self- interactions, we quantify how collisionality changes the effective viscosity and the resulting suppression of PGW power at long, intermediate and short wavelengths. For ULAs, we emphasise that, at linear order and in the minimal (minimally-coupled) sce- nario, the scalar field does not source an anisotropic stress; instead the leading effect on GW propagation arises indirectly via a modification of the background expansion. ULAs behave like an effective vacuum ( w ≃ −1 ) while the field is frozen and then transition to matter-like behaviour ( w ≃ 0 ) when oscillations commence at aosc. This transition changes a′′/a and the conformal friction term in the evolution equation for GWs, producing a step-like feature in the GW transfer function for modes that enter the horizon near the onset of oscillations. We generalise existing theoretical frameworks to incorporate these two physical mechanisms, and we present results across the relevant regimes from super-horizon to sub-horizon scales and from relativistic to non-relativistic phases. Our findings show that ULAs and SIDM produce char- acteristic imprints on the stochastic GW background, ULAs primarily through a background- driven step near k ∼ 1/τosc, and SIDM through modified damping and phase shifts associated with collisional suppression of anisotropic stress. However that the amplitude of these effects is in general too small to be detectable. Crucially, even when they lie below current detection thresholds, recognising and quantifying these signatures is important: they encode complemen- tary microphysical information about dark matter and must be accounted for when interpreting future, increasingly precise measurements of the primordial GW spectrum.