Dark Matter: from the Universe to the Lattice

暗物质支配着宇宙的结构，从最小的星系到可观测的宇宙。通过暗物质对可见恒星和气体的引力作用，我们可以推断暗物质占宇宙总物质的85%。然而，尽管高能、低能实验和天文观测等科学研究不断深入，暗物质的微观物理性质仍然未知。虽然暗物质是通过引力而存在的，但揭示其本质的关键在于探测它在引力之外的相互作用。这一理论物理学的建议侧重于暗物质和暗扇区的粒子物理学和天体物理学。在这个假设下，暗物质粒子之间有相互作用和力，类似于可见物质的丰富物理学及其强、弱和电磁相互作用。在这个广泛的主题下，我将追求两个平行的研究目标。

Dark matter governs the structure of the cosmos, from the smallest galaxies to the observable Universe. Through its gravitational pull on visible stars and gas, we can infer that dark matter makes up 85% of the total matter in the Universe. However, the microphysical properties of dark matter remain unknown despite intense scientific inquiry spanning high and low energy experiments and astronomical observations. While it is firmly established that dark matter exists through its gravity, the key to uncovering its nature lies in detecting its interactions beyond gravity. This proposal in theoretical physics focuses on the particle physics and astrophysics of dark matter and dark sectors. Under this hypothesis, dark matter particles have interactions and forces among themselves, analogous to the rich physics of visible matter and its strong, weak, and electromagnetic interactions. Under this broad theme, I will pursue two parallel research objectives. First, I will investigate tidal streams in the Milky Way as a probe of dark matter substructure. Tidal streams are the tidally-disrupted remnants of globular clusters, which, being dynamically fragile, are easily disrupted by dark matter clumps in the Milky Way. Therefore, tidal streams provide a method for detecting invisible substructures predicted to exist for dark matter that are otherwise completely invisible since they are too small to bind stars and gas on their own. Depending on the underlying particle model for dark matter, clumps are predicted to be concentrated or diffuse or absent altogether. This physics may be related to the long-standing core-cusp problem for rotation curves in galaxies. These observations are consistent with the dark sector model for cored dark matter profiles that more diffuse compared to the cuspy profiles predicted theoretically. However, the jury is still out due to the confounding influence of gas and stars. I will look to tidal streams to settle this controversy once and for all. Free from the confounding effect of stars and gas, tidal streams have the potential to measure the density profiles for substructures that purely dark matter. Second, I will explore the physics of strongly-interacting dark sectors. Dark matter models along these lines are appealing theoretically, but remain under-explored due to the breakdown of the usual Feynman-diagram-based approaches. I will use lattice field theory to study the interactions of dark matter particles within a minimal strongly-interacting dark sector. I will investigate the formation of dark elements through fusion between dark matter particles. I will also calculate the scattering cross section for dark matter particles with one another. These effects can influence phenomenology and astrophysics of dark matter, potentially providing new signatures for discovering its properties.