Nonequilibrium dynamics of axionlike particles: The quantum master equation
Shuyang Cao, D. Boyanovsky
Abstract
We study the nonequilibrium dynamics of axionlike particles (ALP) coupled to Standard Model degrees of freedom in thermal equilibrium. The quantum master equation (QME) for the ALP reduced density matrix is derived to leading order in the coupling of the ALP to the thermal bath, but to all orders of the bath couplings to degrees of freedom within or beyond the Standard Model other than the ALP. The QME describes the damped oscillation dynamics of an initial misaligned ALP condensate, thermalization with the bath, decoherence, and entropy production within a unifying framework. The ALP energy density $\mathcal{E}(t)$ features two components: a ``cold'' component from the misaligned condensate and a ``hot'' component from thermalization with the bath, with $\mathcal{E}(t)={\mathcal{E}}_{c}{e}^{\ensuremath{-}\ensuremath{\gamma}(T)t}+{\mathcal{E}}_{h}(1\ensuremath{-}{e}^{\ensuremath{-}\ensuremath{\gamma}(T)t})$ thus providing a ``mixed dark matter'' scenario. Relaxation of the ALP condensate, thermalization, decoherence, and entropy production occur on similar timescales. An explicit example with ALP-photon coupling, valid post recombination yields a relaxation rate $\ensuremath{\gamma}(T)$ with a substantial enhancement from thermal emission and absorption. A misaligned condensate is decaying at least since recombination and on the same timescale thermalizing with the cosmic microwave background (CMB). Possible consequences for birefringence of the CMB and ALP contribution to the effective number of ultrarelativistic species and galaxy formation are discussed.