  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 by
observation. 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 axions
is produced by flaton decay, which at nucleosynthesis is equivalent to some
number \delta N_\nu of extra neutrino species. Focussing 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 \delta N_\nu in terms of the parameters (masses and couplings).
The KSVZ case is probably already ruled out by the existing bound \delta
N_\nu\lsim 1. The DFSZ case is allowed in a significant region of parameter
space, and will provide a possible explanation for any future detection of
nonzero $\delta N_\nu$.
