Number Counts and Non-Gaussianity

TL;DR

This paper introduces a general method to use object number counts, like primordial black holes and minihalos, to constrain the statistical properties of primordial fluctuations, especially non-Gaussianity, on small scales.

Contribution

It presents a novel procedure to connect number counts of cosmic objects with the probability distribution of primordial fluctuations, including non-Gaussian features.

Findings

Ultracompact minihalos give stronger constraints than primordial black holes.

Constraints on the power spectrum and skewness are derived for different non-Gaussian models.

The method allows probing small-scale primordial fluctuation statistics.

Abstract

We describe a general procedure for using number counts of any object to constrain the probability distribution of the primordial fluctuations, allowing for generic weak non-Gaussianity. We apply this procedure to use limits on the abundance of primordial black holes and dark matter ultracompact minihalos (UCMHs) to characterize the allowed statistics of primordial fluctuations on very small scales. We present constraints on the power spectrum and the amplitude of the skewness for two different families of non-Gaussian distributions, distinguished by the relative importance of higher moments. Although primordial black holes probe the smallest scales, ultracompact minihalos provide significantly stronger constraints on the power spectrum and so are more likely to eventually provide small-scale constraints on non-Gaussianity.