Pinning down the axion

Abstract

Davis has argued that, without inflation, the decay of axionic strings is the primary source of axions. This implies a cosmological lower bound on the axion mass of 10 −5 to 10 −3 eV. In order to obtain a sharper bound it is essential to know the spectrum of emitted axions and the detailed motion of a global string strongly coupled to the axionic field. To this end, we obtain self-consistent, renormalized equations that describe the dynamics of a radiating global string interacting with its surrounding axionic field. We describe the numerical formalism for evolving string trajectories using these equations. From the numerical and analytical evidence we argue that, with appropriate renormalization, the motion of an interacting cosmic string loop can be well approximated by the motion of a free Nambu-Goto string. This implies a lower bound for the axion mass of 10 −3 eV. Together with the recent upper bound of 4 × 10 −4 eV from the supernova SN1987a, this marginally rules out the invisible axion, or at least pins down the axion mass to a very narrow window around 10 −3 eV. This still leaves open the window around 2 eV for hadronic axions, but in that case the axion is no longer a serious dark matter candidate.