Contrasting galaxy formation from quantum wave dark matter, ψDM, with ΛCDM, using Planck and Hubble data

The newly established luminosity functions (LFs) of high-z galaxies at 4 ≲ z ≲ 10 can provide a stringent check on dark matter models that aim to explain the core properties of dwarf galaxies. The cores of dwarf spheroidal galaxies are understood to be too large to be accounted for by free streaming of warm dark matter without overly suppressing the formation of such galaxies. Here we demonstrate with cosmological simulations that wave dark matter, $\psi DM$, appropriate for light bosons such as axions, does not suffer from this problem, given a boson mass of $m_{\psi }⩾1.2\times {10}^{-22}eV$ (2σ). In this case, the halo mass function is suppressed below $\sim {10}^{10}{M}_{\odot }$ at a level that is consistent with the high-z LFs, while simultaneously generating the kiloparsec-scale cores in dwarf galaxies arising from the solitonic ground state in $\psi DM$. We demonstrate that the reionization history in this scenario is consistent with the Thomson optical depth recently reported by Planck, assuming a reasonable ionizing photon production rate. We predict that the LF should turn over slowly around an intrinsic ultraviolet luminosity of $M_{UV}\gtrsim -16$ at $z\gtrsim 4$. We also show that for galaxies magnified $>10\times$ in the Hubble Frontier Fields, $\psi DM$ predicts an order of magnitude fewer detections than cold dark matter at $z\gtrsim 10$ down to $M_{UV}\sim -15$, allowing us to distinguish between these very different interpretations for the observed coldness of dark matter.