Thermodynamics and inflation
The standard model of particle physics is introduced, and extensions of it, which may be of cosmological relevance, are considered. The inflationary paradigm is reviewed as an extension of the standard cosmological model. In particular, the natural inflation mechanism resulting from a thermal phase change in a field theory with a spontaneous symmetry breaking potential, is examined. The question of when thermal equilibrium is likely to be a valid assumption in the early universe is considered in some detail. For inflation models, this question is answered by a self-consistency argument involving the total number of interactions per inflaton particle. In order to describe thermal-phase-change inflation models further, the temperature-dependent effective potential resulting from finite-temperature field theory is reviewed. The self-consistency test is developed into a numerical procedure which may be used to discuss the likelihood of thermal state generation in specific inflation models in a quantitative way. Alternatively, the method can be used to provide bounds on the parameters in the inflation potential from the requirement that a thermal state should occur. This procedure is applied to several example potentials and in particular it is easily verified that the "new inflation" model (relying on a phase change) is not viable. The method is quite general and can be applied to any inflation model for which a finite temperature effective potential can be defined. The procedure is generalised to the recently proposed extended inflation. Bounds on the extra free parameters which must be introduced in extended inflation are discussed. It is concluded that despite these extra free parameters the difficulties of generating a thermal state are just as great as they are in conventional inflation.