  Infrared dressing of bosonic or fermionic heavy particles by a cloud of
massless particles to which they couple is studied as a possible production
mechanism of ultra light dark matter or dark radiation in a radiation dominated
cosmology. We implement an adiabatic expansion valid for wavelengths much
smaller than the Hubble radius combined with a non-perturbative and manifestly
unitary dynamical resummation method to study the time evolution of an initial
single heavy particle state. We find a striking resemblance to the process of
particle decay: the initial amplitude of the single particle decays in time,
not exponentially but with a power law with anomalous dimension $\propto
t^{-\Delta/2}$ featuring a crossover to $t^{-\Delta}$ as the heavy particle
becomes non-relativistic in both bosonic and fermionic cases suggesting certain
universality. At long time the asymptotic state is an entangled state of the
heavy and massless particles. The entanglement entropy is shown to grow under
time evolution describing the flow of information from the initial single
particle to the final multiparticle state. The expectation value of the energy
momentum tensor in the asymptotic state is described by two indpendent fluids
each obeying covariant conservation, one of heavy particles and the other of
relativistic (massless) particles (dark radiation). Both fluids share the same
frozen distribution function and entropy as a consequence of entanglement.
