Thesis (Ph. D. in Physics)--Vanderbilt University, May 2004. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [112]-119).

The modern fields of 𝜸-ray astrophysics, multi-messenger astronomy, and particle astrophysics, have a shared history and future. This thesis will focus on the interconnectedness between them, and the role that measurements of very high-energy (VHE; 100 GeV < 𝐸 < 100 TeV) 𝜸 rays play in contributing to them. In particular, one confirmed and one putative source class for VHE 𝜸 rays will be explored: active galactic nuclei (AGN) and short gamma-ray bursts (sGRBs) (associated binary neutron star (BNS) merger progenitors), characterized by their variable and transient emission behavior respectively. The particle acceleration and radiative processes which can result in this energetic electromagnetic (EM) emission in these sources is described. Subsequently, the detection principles of VHE 𝜸-ray photons is detailed, highlighting the unique detection technique of imaging atmospheric Cherenkov telescopes (IACTs) to use the Earth’s atmosphere as an effective high-energy particle calorimeter. Advancements in the field of these detectors will be discussed, from the first-generation of detectors up to its current generation, which includes the VERITAS 𝜸-ray observatory, the principal instrument used to conduct the analyses in this thesis. Additionally, a prototype for the novel two-mirror Schwarzschild-Couder telescope (SCT) design will be introduced, which is proposed for inclusion in the future Cherenkov Telescope Array Observatory (CTAO), set to be the next-generation observatory for VHE 𝜸 rays. Finally, work from three projects, each demonstrating the contributions VHE ? rays can make to the initially listed fields, will be discussed. First, a multi-messenger search for VHE 𝜸-ray emission in VERITAS associated with sub-threshold gravitational wave (GW) signals. No VHE ?-ray emission is detected; the upper limit on the integral flux for all VERITAS observations is reported and compared to a sGRB model. Next, a search for the imprint of beyond-the-standard-model axion-like particles (ALPs) on the flaring VHE spectrum of the radio galaxy (RG) AGN NGC 1275, embedded in the cool-core Perseus cluster. No detection is made; limited exclusions on the mass and coupling strength to electromagnetism are reported. Finally, a VERITAS detection of a VHE ?-ray flare from the blazar AGN B2 1811+31 will be presented. Preliminary work from the broadband analysis of the source are shown, and the future of the project is discussed.