Role of QCD in moduli stabilization during inflation and axion dark matter

Abstract

Ignorance of the initial condition for the axion dynamics in the early Universe has led us to consider an O(1) valued initial amplitude, and that prefers the decay constant, Fa, of the QCD axion to be an intermediate scale such as 1012 GeV in order to explain the dark matter abundance. We explore a cosmological scenario of Fa being much larger than 1012 GeV by considering the axion and modulus dynamics during inflation to set the initial amplitude. We show that if the volume modulus (radion) of the extra-dimension is stabilized mainly by the QCD contribution to the modulus potential during inflation, the QCD axion with the string-scale decay constant obtains a mass around the inflationary Hubble parameter. This means that the axion rolls down to the θ = 0 minimum during the inflation realizing almost vanishing initial amplitude, and the inflationary quantum fluctuation can be the dominant source of the current number density of axions. We find natural parameter regions where the axion explains the cold dark matter of the Universe, while the constraint on the isocurvature perturbation is avoided. The presence of the axion miniclusters or axion stars are predicted in a wide range of parameters, including the one explains the Subaru-HCS microlensing event.