Green's function of the cosmological thermalization problem
  Energy release in the early Universe leads to spectral distortions of the
cosmic microwave background (CMB) which in the future might allow probing
different physical processes in the pre-recombination (z>~10^3) epoch.
Depending on the energy injection history, the associated distortion partially
thermalizes due to the combined action of Compton scattering, double Compton
scattering and Bremsstrahlung emission, a problem that in general is hard to
solve. Various analytic approximations describing the resulting distortion
exist, however, for small distortions and fixed background cosmology the
Green's function of the problem can be pre-computed numerically. Here we show
that this approach gives very accurate results for a wide range of thermal
histories, allowing fast and quasi-exact computation of the spectral distortion
given the energy release rate. Our method is thus useful for forecasts of
possible constraints on early-universe physics obtained from future
measurements of the CMB spectrum.
