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The far infrared physics is a fascinating topic for theoretical physics,since the foundation of quantum field theory and neutrinos seem to be stronglyrelated with the far infrared physics of our Universe. In this work we shallexplore the possibility of a late-time thermal phase transition caused by theaxion-neutrino interactions. The axion is assumed to be the misalignment axionwhich is coupled primordially to a chiral symmetric neutrino. The chiralsymmetry is supposed to be broken either spontaneously or explicitly, and twodistinct phenomenological models of axion-neutrinos are constructed. The axionbehaves as cold dark matter during all its evolution eras, however if we assumethat the axion and the neutrino fields interact coherently in a classical wayas fields, or as ensembles, then we consider thermal effects in the axionsector, due to the values of operators $\phi$ for the axion and $\bar{\nu}\nu$due to the neutrinos. The thermal equilibrium between the two has no effect tothe axion effective potential for a wide temperature range. As we show,contrary to the existing literature, the axion never becomes destabilized dueto the finite temperature effects, however if axion-Higgs higher ordernon-renormalizable operators are present in the Lagrangian, the axion potentialis destabilized in the temperature range $T\sim 0.1\,$MeV down to $T\sim0.01\,$eV and a first order phase transition takes place. The initial axionvacuum decays to the energetically more favorable axion vacuum, and the latterdecays to the Higgs vacuum which is more preferable. This late-time phasetransition might take place in the redshift range $z\sim 385-37$ and thus itmay cause density fluctuations in the post-recombination era.

Axion-Neutrino Couplings, Late-time Phase Transitions and the Far Infrared Physics