Silk damping at a redshift of a billion: a new limit on small-scale adiabatic perturbations

We study the dissipation of small-scale adiabatic perturbations at early times when the Universe is hotter than T ~ 0.5 keV. When the wavelength falls below the damping scale 1/kD, the acoustic modes diffuse and thermalize, causing entropy production. Before neutrino decoupling, kD is primarily set by the neutrino shear viscosity, and we study the effect of acoustic damping on the relic neutrino number, primordial nucleosynthesis, dark-matter freeze-out, and baryogenesis. This sets a new limit on the amplitude of primordial fluctuations of DeltaR^2 < 0.007 at 10^4/Mpc< k < 10^5/Mpc and a model dependent limit of DeltaR^2 < 0.3 at k < 10^{20-25}/Mpc.