To Relativity and Beyond: Hunting for Gravitational Wave signatures of Physics beyond General Relativity

Abstract

This thesis develops and applies diagnostic frameworks to place constraints on a broad class of theories beyond General Relativity utilizing gravitational wave probes across a hierarchy of physical scales. At the level of perturbation theory, the tidal response of black holes is investigated in the presence of additional degrees of freedom. By extending the formalism to include non-minimally coupled vector-tensor fields, we demonstrate the existence of hidden underlying symmetries, offering novel use cases for future Earth-based detection efforts. Transitioning to galactic scales, our attention is turned to the Stochastic Gravitational Wave Background within the nano-Hertz frequency band, a regime typically accessible to Pulsar Timing Array experiments. The impact of gravitational wave dispersion on the spectral shape of the background is analyzed, establishing a methodology to place constraints on modified gravity theories using future timing datasets. On cosmological scales, the generation of second-order induced gravitational waves via inflationary magnetogenesis is examined. We demonstrate that deviations from the traditional slow-roll paradigm may induce significant enhancements to the gravitational wave energy density, serving as a unique probe of the early Universe’s equation of state. Collectively, this work seeks to highlight the necessity of a multi-band approach to con-straining new models of General Relativity synthesizing constraints from source dynamics, propagation, and primordial initial conditions.