The effective gravitational decoupling between dark matter and the CMB
  We present a detailed and self-contained analytical derivation of the
evolution of sub-horizon cosmological perturbations before decoupling, based on
previous work by S. Weinberg. These solutions are valid in the minimal LCDM
scenario, to first order in perturbation theory, in the tight-coupling limit
and neglecting neutrino shear stress. We compare them to exact numerical
solutions computed by a Boltzmann code, and we find the two to be in very good
agreement. The analytic solutions show explicitly that CDM and the
baryon-photon fluid effectively behave as separate self-gravitating fluids
until the epoch of baryon drag. This in turn leads to the surprising conclusion
that the CMB is much less sensitive to the clustering properties of minimally
coupled Dark Matter models than what would be naively expected.
