Impact of Sommerfeld Corrections on the Dark Matter Relic Density

This thesis explores how long‑range self‑interactions modify the standard thermal freeze‑out picture of dark matter via the non‑perturbative Sommerfeld effect. After a concise but thorough review of the astrophysical and cosmological evidence for cold dark matter—and of the broad landscape of particle‑physics candidates—we focus on the so‑called Minimal Dark Matter scenario, in which a single electroweak multiplet, with no ad hoc couplings beyond gauge interactions, constitutes the dark sector. We then derive the Sommerfeld enhancement factor from first principles in quantum field theory, carefully relating the resummation of ladder diagrams to the non‑relativistic Schrödinger formalism. Armed with this general framework, we revisit the Minimal Dark Matter relic‑density calculation: our approach reproduces the classic results and clarifies the interplay between gauge‑boson masses, mass splittings, and low‑velocity annihilation rates. The latter part of the thesis extends this formalism to dark matter frameworks where Sommerfeld corrections have not yet been computed, providing new insights into their potential impact on dark matter relic density.