Dark Matter Substructure as a Window to Fundamental Physics

The matter power spectrum on small scales (< 1 Mpc) is very weakly constrained so far. While inflation predicts a nearly scale-invariant primordial power spectrum down to very small scales, many new physics scenarios can lead to significantly different predictions, such as axion dark matter in the post-inflationary scenario, vector dark matter produced during inflation, early matter domination, kinetic misalignment axions, self-interacting dark matter, atomic dark matter, etc. Therefore, any successfully measurement on the matter power spectrum is not only testing inflation extensively, but also probe early Universe dynamics and the nature of dark matter, which makes it a new frontier in cosmology and dark matter physics. We proposed observing fast radio bursts (FRB) with solar-system scale interferometry by sending radio telescopes to space, which allows us to greatly expand the sensitivity on the matter power spectrum from Mpc to AU scales. Two sightlines looking at the same FRB source can sample different region of the Universe on the transverse direction and thus obtain an arrival time difference that depends on the matter power spectrum. Our calculations show that this setup will be sensitive to the scale-invariant power spectrum predicted by inflation on extremely small scales and can also probe QCD axion miniclusters predicted in the post-inflationary scenario.