Constraints on Primordial Power Spectrum from Galaxy Luminosity
  Functions
  We derive constraints on primordial power spectrum, for the first time, from
galaxy UV luminosity functions (LFs) at high redshifts. Since the galaxy LFs
reflect an underlying halo mass function which depends on primordial
fluctuations, one can constrain primordial power spectrum, particularly on
small scales. We perform a Markov Chain Monte Carlo analysis by varying
parameters for primordial power spectrum as well as those describing
astrophysics. We adopt the UV LFs derived from Hubble Frontier Fields data at
$z = 6 -10$, which enable us to probe primordial fluctuations on the scales of
$k \sim 10 - 10^3~{\rm Mpc}^{-1}$. Our analysis also clarifies how the
assumption on cosmology such as primordial power spectrum affects the
determination of astrophysical parameters.
