Early universe dynamics of PQ field with very small self-coupling and its implications for axion dark matter
Axion-like particles (ALPs) are often considered as good candidates for dark matter. Several mechanisms generating relic abundance of ALP dark matter have been proposed. They may involve processes which take place before, during or after cosmic inflation. In all cases an important role is played by the potential of the corresponding Peccei-Quinn (PQ) field. Quite often this potential is assumed to be dominated by a quartic term with a very small coupling. We show that in such situation it is crucial to take into account different kinds of corrections especially in models in which the PQ field evolves during and after inflation. We investigate how such evolution changes due to radiative, thermal and geometric corrections. In many cases those changes are very important and result in strong modifications of the predictions of a model. They may strongly influence the amount of ALP contributions to cold and warm components of dark matter as well as the power spectrum of associated isocurvature perturbations. Models with a quasi-supersymmetric spectrum of particles to which the PQ field couples seem to be especially interesting. Qualitative features of such models are discussed with the help of approximate analytical formulae. However, the dynamics of the PQ field with the considered corrections taken into account is more complicated than in the case without corrections so dedicated numerical calculations are necessary to obtain precise predictions. We present such results for some characteristic benchmark points in the parameter space.