Dark Matter: from the Universe to the Lattice

暗物质主宰着宇宙的结构，从最小的星系到可见的宇宙，通过它对可见恒星和气体的引力，我们可以推断暗物质占宇宙总物质的85%。然而，尽管进行了跨越高能和低能的密集科学调查、实验和天文观测，但暗物质的微观物理性质仍然未知。虽然人们坚定地认为暗物质是通过其引力存在的，但揭示其本质的关键在于检测其超出引力的相互作用。理论物理中的这一提议侧重于暗物质和暗扇区的粒子物理和天体物理。在这一假设下，暗物质粒子之间存在相互作用和作用力，类似于可见物质的丰富物理学及其强、弱和电磁相互作用。在这一大主题下，我将追求两个平行的研究目标。首先，我将研究银河系中的潮汐流，作为暗物质亚结构的探测器。潮汐流是球状星团被潮汐破坏的残余物，它们在动态上很脆弱，很容易被银河系中的暗物质团破坏。因此，潮汐流提供了一种方法来探测暗物质中预计存在的不可见的子结构，否则这些子结构是完全看不见的，因为它们太小了，不能自己束缚恒星和气体。根据暗物质的基本粒子模型，团块被预测为集中或扩散或完全不存在。这一物理学可能与星系自转曲线长期存在的核心-尖点问题有关。这些观测结果与暗物质核心轮廓的暗扇区模型是一致的，与理论上预测的尖峰轮廓相比，暗物质轮廓更加弥散。然而，由于气体和恒星的混杂影响，陪审团仍然没有定论。我将指望潮流一劳永逸地解决这一争议。没有恒星和气体的混杂效应，潮汐流有可能测量纯粹暗物质的子结构的密度分布。其次，我将探索强相互作用暗扇区的物理学。这些暗物质模型在理论上很有吸引力，但由于通常的基于费曼图的方法的崩溃，这些模型仍然没有得到充分的探索。我将使用格子场理论来研究最小的强相互作用暗扇区内暗物质粒子的相互作用。我将通过暗物质粒子之间的聚变来研究暗元素的形成。我还将计算暗物质粒子相互之间的散射截面。这些效应可能会影响暗物质的现象学和天体物理学，可能会为发现其性质提供新的信号。

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.