Large change in the predicted number of small halos due to a small amplitude oscillating inflaton potential

Abstract

A smooth inflaton potential is generally assumed when calculating the primordial power spectrum, implicitly assuming that a very small oscillation in the inflaton potential creates a negligible change in the predicted halo mass function. We show that this is not true. We find that a small oscillating perturbation in the inflaton potential in the slow-roll regime can alter significantly the predicted number of small halos. A class of models derived from supergravity theories gives rise to inflaton potentials with a large number of steps and many trans-Planckian effects may generate oscillations in the primordial power spectrum. The potentials we study are the simple quadratic (chaotic inflation) potential with superimposed small oscillations for small field values. Without leaving the slow-roll regime, we find that for a wide choice of parameters, the predicted number of halos change appreciably. For the oscillations beginning in the ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$ range, for example, we find that only a 5% change in the amplitude of the chaotic potential causes a 50% suppression of the number of halos for masses between ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$ and an increase in the number of halos for masses $<{10}^{6}{M}_{\ensuremath{\bigodot}}$ by factors $\ensuremath{\sim}15--50$. We suggest that this might be a solution to the problem of the lack of observed dwarf galaxies in the range ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$. This might also be a solution to the reionization problem where a very large number of Population III stars in low mass halos are required.