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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_a of order 10^{10}GeV and generic flaton models give F_a of order 10^9 GeV as required byobservation. The axion is a good candidate for cold dark matter in all cases,because its density is diluted by flaton decay if F_a is bigger than 10^{12}GeV. In addition to the dark matter axions, a population of relativistic axionsis produced by flaton decay, which at nucleosynthesis is equivalent to somenumber \delta N_\nu of extra neutrino species. Focussing on the canonicalmodel, containing three flaton particles and two flatinos, we evaluate all ofthe flaton-flatino-axion interactions and the corresponding axionic decayrates. They are compared with the dominant hadronic decay rates, for both DFSZand KSVZ models. These formulas provide the basis for a precise calculation ofthe equivalent \delta N_\nu in terms of the parameters (masses and couplings).The KSVZ case is probably already ruled out by the existing bound \deltaN_\nu\lsim 1. The DFSZ case is allowed in a significant region of parameterspace, and will provide a possible explanation for any future detection ofnonzero $\delta N_\nu$

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