Stringent constraints on intra-galactic substructure and the primordial power spectrum from ultra-faint dwarf dynamics

It is important to confront the most pessimistic scenario for dark matter, in which it interacts with ordinary matter only through gravity. Even in this case, both the particle physics of dark matter and aspects of our cosmological history can be probed through its gravitational imprint, in particular its small-scale substructure. In this talk, I present stringent constraints on such substructure derived from the absence of observable heat exchange between dark-matter substructure in ultra-faint dwarf galaxies and their stellar populations. Such heating would lead to an expansion of the stellar half-light radius beyond what is observed. These constraints translate into orders-of-magnitude improvements on limits to the primordial power spectrum down to kiloparsec scales. The results also have important implications for dark-matter self-interactions and other microphysical properties that can enhance small-scale structure.