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A smooth inflaton potential is generally assumed when calculating theprimordial power spectrum, implicitly assuming that a very small oscillation inthe inflaton potential creates a negligible change in the predicted halo massfunction. We show that this is not true. We find that a small oscillatingperturbation in the inflaton potential in the slow-roll regime can altersignificantly the predicted number of small halos. A class of models derivedfrom supergravity theories gives rise to inflaton potentials with a largenumber of steps and many transplanckian effects may generate oscillations inthe primordial power spectrum. The potentials we study are the simple quadratic(chaotic inflation) potential with superimposed small oscillations for smallfield values. Without leaving the slow-roll regime, we find that for a widechoice of parameters, the predicted number of halos change appreciably. For theoscillations beginning in the 10^7-10^8 solar masses range, for example, wefind that only a 5% change in the amplitude of the chaotic potential causes a50% suppression of the number of halos for masses between 10^7-10^8 solarmasses and an increase in the number of halos for masses <10^6 solar masses byfactors ~15-50. We suggest that this might be a solution to the problem of thelack of observed dwarf galaxies in the range 10^7-10^8 solar masses. This mightalso be a solution to the reionization problem where a very large number ofPopulation III stars in low mass halos are required.

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