Signals from the Dark Sector: A Phenomenological Study of ALPs, Ultralight Fields, and Minimal Dark Matter

The Standard Model of particle physics, while remarkably successful, is incomplete. Among all hints towards physics beyond the Standard Model, dark matter (DM) stands out due to overwhelming astrophysical and cosmological evidence for its existence. This thesis tackles the fundamental nature of DM through a multi-faceted investigation, combining theoretical model-building with phenomenological studies across complementary detection channels. We first explore the connection between gravitational wave astronomy and ultralight dark matter (ULDM) by analyzing the stochastic gravitational wave background reported by pulsar timing arrays, placing new constraints on ULDM particle masses in the range 1.3 × 10^{-21} eV ≲ m ≲ 1.4 × 10^{-20} eV, thereby demonstrating the potential of gravitational waves as a precision probe for DM. We then investigate a particular family of leptophobic, anomaly-free axion-like particles (ALPs) as DM candidates, showing that while this family provides a compelling candidate, it can be probed in the near future through rare decay experiments like NA62 and X-ray observatories. Furthermore, we study the potential of a thermal fermionic dark matter candidate that interacts with the Standard Model through an ALP portal to explain the longstanding 511 keV astrophysical anomaly; this model, where light thermal DM annihilates into intermediate ALPs that decay into low-energy positrons, provides a viable explanation for the observed gamma-ray line from the Galactic Center while evading constraints from continuum emission and cosmological limits. Finally, we revisit the well-motivated Weakly Interacting Massive Particle (WIMP) paradigm within the Minimal Dark Matter framework, performing an improved calculation of the gamma-ray spectrum from the annihilating electroweak 5-plet that includes next-to-leading order corrections and bound-state formation effects. Our analysis shows that current data from Fermi-LAT already constrains this model, and we project that the upcoming Cherenkov Telescope Array Observatory will decisively test its viability. Collectively, this work underscores the necessity of a diverse and synergistic approach to dark matter discovery, bridging particle physics, cosmology, and astrophysics to refine theoretical frameworks and guide future experimental searches.