AxionH0graphy: hunting for ultralight dark matter with cosmographic H$_0$ signal

If ultralight boson fields exist, then vacuum misalignment populates them with nonzero relic abundance. For a broad range of particle mass $m$ the field condenses into fuzzy cores in massive galaxies. We use numerical simulations to test this idea, extending previous work (Blum and Teodori 2021) and focusing on ultralight dark matter (ULDM) that makes-up a subdominant fraction of the total dark matter density, consistent with observational constraints. Our simulations mimic galactic halos and explore different initial conditions and levels of sophistication in the modeling of the halo potential. For $m\sim10^{-25}$ eV ULDM cores act as approximate internal mass sheets in strong gravitational lensing, and could first be detected as an $H_0$ bias in cosmography: a scenario we dub AxionH0graphy. The mass sheet degeneracy is broken by finite core radius and by the dynamical displacement of cores from the halo center of mass, which introduce imaging distortions and restrict the $H_0$ bias limit of AxionH0graphy to $m\lesssim5\times10^{-25}$ eV. Cosmological simulations are called for to sharpen the predicted connection between the amplitude of ULDM galactic cores and the ULDM cosmological fraction.