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We provide a simple but robust bound on the primordial curvature perturbationin the range $10^4 {\rm Mpc}^{-1} < k < 10^5 {\rm Mpc}^{-1}$, which has notbeen constrained so far unlike low wavenumber modes. Perturbations on thesescales dissipate the energy of their acoustic oscillations by the Silk dampingafter primordial nucleosynthesis but before the redshift $z \sim 2 \times 10^6$and reheat the photon bath without invoking CMB distortions. This {\it acousticreheating} results in the decrease of the baryon-photon ratio. By combiningindependent measurements probing the nucleosynthesis era and around therecombination epoch, we find an upper bound on the amplitude of the curvatureperturbation over the above wavenumber range as ${\cal P}_\zeta < 0.06$.Implications for super massive black holes are also discussed.

Reheating the Universe Once More: The Dissipation of Acoustic Waves as a Novel Probe of Primordial Inhomogeneities on Even Smaller Scales