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.
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