Axion minicluster power spectrum and mass function

TL;DR

This paper develops a semi-analytical framework to predict the power spectrum and mass distribution of axion miniclusters formed after PQ symmetry breaking, providing detailed mass and size ranges for these objects.

Contribution

It introduces a modified Press & Schechter method and a semi-analytical approach to accurately model axion minicluster formation and properties during radiation domination.

Findings

Minicluster masses range from 5×10^{-16} to 3×10^{-13} solar masses.

Minicluster sizes range from 4×10^4 to 7×10^5 km.

The model predicts detailed mass and size distributions based on PQ scale.

Abstract

When Peccei-Quinn (PQ) symmetry breaking happens after inflation, the axion field takes random values in causally disconnected regions. This leads to fluctuations of order one in the axion energy density around the QCD epoch. These over-densities eventually decouple from the Hubble expansion and form so-called miniclusters. We present a semi-analytical method to calculate the average axion energy density, as well as the power spectrum, from the re-alignment mechanism in this scenario. Furthermore, we develop a modified Press & Schechter approach, suitable to describe the collapse of non-linear density fluctuations during radiation domination, which is relevant for the formation of axion miniclusters. It allows us to calculate the double differential distribution of gravitationally collapsed miniclusters as a function of their mass and size. For instance, assuming a PQ scale of $10^{11}$ GeV, minicluster masses range from about $5 \times 10^{-16}$ to $3 \times 10^{-13}$ solar masses and have sizes from about $4\times 10^4$ to $7\times 10^5$ km at the time they start to collapse.