Some aspects of thermal in ation : the nite temperature potential and topological defects

Currently favoured extensions of the Standard Model typically contain ` aton elds' de ned as elds with large vacuum expectation values (vevs) and almost at potentials. If a aton eld is trapped at the origin in the early universe, one expects `thermal in ation' to take place before it rolls away to the true vacuum, because the nite-temperature correction to the potential will hold it at the origin until the temperature falls below 1TeV or so. In the rst part of the paper, that expectation is con rmed by an estimate of the nite temperature corrections and of the tunneling rate to the true vacuum, paying careful attention to the validity of the approximations that are used. The second part of the paper considers topological defects which may be produced at the end of an era of thermal in ation. If the aton elds associated with the era are GUT higgs elds, then its end corresponds to the GUT phase transition. In that case, the abundance of monopoles and of GUT higgs particles will have to be diluted by a second era of thermal in ation (or perhaps some non-thermal analogue). Such an era will not a ect the cosmology of GUT strings, for which the crucial parameter is the