Abundance of relativistic axions in a flaton model of Peccei-Quinn symmetry

Flaton models of Peccei-Quinn symmetry have good particle physics motivation, and are likely to cause thermal inflation leading to a well-defined cosmology. They can solve the {μ} problem, and generate viable neutrino masses. Canonical flaton models predict an axion decay constant FPQ~10¹⁰ GeV and generic flaton models give FPQ10⁹ GeV as required by observation. The axion is a good candidate for cold dark matter in all cases, because its density is diluted by flaton decay if FPQ10¹² GeV. In addition to the dark matter axions, a population of relativistic axions is produced by flaton decay, which at nucleosynthesis is equivalent to some number δN_ν of extra neutrino species. Focusing on the canonical model, containing three flaton particles and two flatinos, we evaluate all of the flaton-flatino-axion interactions and the corresponding axionic decay rates. They are compared with the dominant hadronic decay rates, for both DFSZ and KSVZ models. These formulas provide the basis for a precise calculation of the equivalent δN_ν in terms of the parameters (masses and couplings). The KSVZ case is probably already ruled out by the existing bound δN_ν1. The DFSZ case is allowed in a significant region of parameter space, and will provide a possible explanation for any future detection of nonzero δN_ν.