Invisible axions and the QCD phase transition in the early Universe

We examine, in detail, the conditions under which the quark-hadron phase transition in the early Universe can influence the previously determined upper bound on the axion decay constant fₐ{}5×{}10¹² GeV. By integrating the axion equation of motion (in general and in a specific model) through the phase transition we find that if the phase transition is sufficiently abrupt the limit on fₐ may change by an order of magnitude in either direction (depending on initial conditions); the most probable result is a tightening of the bound by a factor {~}5. Sensitive axion detectors, as are now being contemplated, could conceivably provide information on the Universe at {~}10^-5 sec after the big bang.