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 kD^-1, 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 ΔR²<0.007 at 10⁴ Mpc^-1k10⁵ Mpc^-1 and a model-dependent limit of ΔR²0.3 at k10²⁰⁻⁻²⁵ Mpc^-1.
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Jeong et al. (2014) studied this question.
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