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 mu problem, and generate viable neutrino masses. Canonical flaton models predict an axion decay constant F(PQ)similar to 10(10) GeV and generic Baton models give F(PQ)greater than or similar to 10(9) CeV as required by observation. The axion is a good candidate for cold dark matter in all cases, because its density is diluted by Baton decay if F(PQ)greater than or similar to 10(12) GeV. In addition to the dark matter axions, a population of relativistic axions is produced by Baton decay, which at nucleosynthesis is equivalent to some number deltaN(nu) 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 deltaN(nu) in terms of the parameters (masses and couplings). The KSVZ case is probably already ruled out by the existing bound deltaN(nu)less than or similar to1. The DFSZ case is allowed in a significant region of parameter space, and will provide a possible explanation for any future detection of nonzero SN,.