Nonequilibrium QFT of axion-like particles and condensates and cosmological constraints on freeze-in and domain wall scenarios

We consider the effect of the interaction between axions and Standard Model parti- cles, specifically their evolution during the earliest stages of the Universe, for three different axion models: the photophilic, photophobic, and GUT heavy axion cases. We analyse their scenarios of freeze-in and the case of axion domain walls created after the QCD phase transition with a domain wall number NDW > 1 and subjected to thermal plasma friction. To handle such effects involving both thermal and non-thermal processes, we develop a theoretical formalism with fully relativistic Boltzmann and modified Gross-Pitaevskii equations for the coupled particle and condensate phase-space distributions, includ- ing self-interactions, in an expanding universe (or general background metric) derived from the 2PI effective action. We solve the coupled equations considering the numerically simplest irreducible scenario of ALPs produced via freeze-in with a low reheating temperature ( T ∼ 5 − 10MeV ) and respecting the limits by the Big Bang Nucleosynthesis (BBN) and the effective number of ultrarelativistic degrees of freedom ∆Neff, keeping care of the evolution of the condensate misalignment angle and the contribution of muons. We derive new bounds for all three models and utilise our formalism to enhance the existing results and relative bounds on the thermal plasma friction acting on the axion domain walls. In the two different scenarios, we solve the equations numerically with MicrOmegas 6.1.15 For the last aspect, we improve upon some known results in the literature by consid- ering the complete quantum equations of motion for the condensate domain wall and the muon contribution relevant for high-mass ALPS, thereby determining the param- eter space where the domain wall problem can be solved through the thermal friction mechanism. In both cases, we get interesting bounds and results in the region of axion mass ma > 1MeV .