Brownian Axion-like Particles

We studied the non-equilibrium dynamics of an axion-like particle (ALP) weakly coupled to a thermal bath and misaligned initial conditions. The ALP’s in-in effective action is obtained to leading order in the ALP coupling to the bath but to all orders in the couplings among the bath’s degrees of freedom. The ALP obeys an effective Langevin equation with noise and friction kernels satisfying the fluctuation dissipation relation. The solution exhibits damping of the misaligned condensate and thermalization with the bath. It describes a mixed dark matter scenario where the initial (cold) component decays and the thermalized (hot) component grows. Specifically, we consider the ALP-photon coupling gaE·B to lowest order, valid from recombination onwards. UV divergences of the ALP self-energy require higher order derivative terms in the effective action. When T>>m_a, the long-wavelength relaxation rate is substantially enhanced Γ_T/Γ₀=4T/m_a and the finite temperature effective ALP mass is m_T²=m_a²[1-(T/T_c)⁴], with T_c∝√(m_a/g), suggesting the possibility of an inverted phase transition, which when combined with higher derivative terms may indicate exotic new phases. These may yield cosmological consequences on structure formation, the effective number of relativistic species and cosmic birefringence.