Phenomenological use of lattice-determined integral moments

Determine how one or two lattice-determined integral moments of the thermal axion production rate can constrain phenomenological observables, particularly how they should be used to convert limits on the number of cosmological radiation degrees of freedom into limits on the axion mass.

Background

The lattice method developed in the paper does not reconstruct the differential axion production rate as a function of momentum. Instead, it yields one or two weighted integrals of the rate through Euclidean correlation functions. The authors explicitly identify the unresolved issue of how useful these integral constraints are for cosmological applications, including the translation of radiation-density limits into axion-mass constraints.