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We study the dissipation of small-scale adiabatic perturbations at early times when the Universe is hotter than T0. 5 keV. When the wavelength falls below the damping scale k₃^-1, the acoustic modes diffuse and thermalize, causing entropy production. Before neutrino decoupling, k₃ 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 ₑ^2<0. 007 at 10^4 Mpc^-110^5 Mpc^-1 and a model-dependent limit of ₑ^20. 3 at k10^20--25 Mpc^-1.
Jeong et al. (Tue,) studied this question.