Search for Dark Matter and Vacuum Quantum Gravity Fluctuations using Gravitational Wave Experiments

The biggest physics discoveries of recent decades—the detection of the Higgs at the Large Hadron Collider (LHC) in 2012 and the observation of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) in 2015—are often celebrated as two monumental yet distinct discoveries. While the potential of gravitational wave experiments to illuminate particle physics has been acknowledged, its full scope has not been fully appreciated. In this dissertation, we explore various methods to utilize experiments designed for gravitational wave observations in the pursuit of understanding physics beyond the standard model. Specifically, we study two pressing aspects of particle physics: dark matter and quantum gravity, examining their potential signatures in these experiments. Pulsars, due to their stable periods, are exceptionally suited for gravitational wave observations. Recently, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) reported positive evidence of a stochastic gravitational wave background in 2023. While the application of pulsar timing measurements in gravitational wave detection is well established, they also offer avenues to study various properties of dark matter, such as the small-scale power spectrum and gravitational wave signatures from a cosmological phase transition. We will discuss search strategies for dark matter using realistic pulsar timing array data, current constraints, and future prospects. Laser interferometry-based gravitational wave detectors like LIGO also offer a potential pathway for dark matter detection. With their high precision in measuring laser phase fluctuations, even feeble interactions between dark matter and standard model particles can produce signals of potentially measurable size. This includes gravitational interactions as well as other long-range forces, such as scalar or vector mediated Yukawa interactions. We will explore the spectral shape of such signals and their detection prospects. Finally, recent proposals suggest that vacuum quantum gravity effects may manifest as observable phenomena at low energies in laser interferometers. Planck-sized fluctuations arising from quantum gravity are amplified by the large number of degrees of freedom on the horizon of the causal diamond, corresponding to its entropy. Although LIGO is nominally sensitive to these signatures, its lack of sensitivity at the free-spectral range frequency of the cavities renders it ill-suited for detecting such phenomena, highlighting the need for additional experimental setups. We will discuss one approach to estimate the size of these fluctuations by drawing connections between a four-dimensional causal diamond and known solutions of two-dimensional Jackiw–Teitelboim (JT) gravity, as well as the experimental implications.