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Probing small-scale non-Gaussianity from anisotropies in acoustic reheating

We give new constraints on small-scale non-Gaussianity of primordial curvature perturbations by the use of anisotropies in acoustic reheating. Mixing of local thermal or local kinetic equilibrium systems with different temperatures yields a locally averaged temperature rise, which is proportional to the square of temperature perturbations damping in the photon diffusion scale. Such secondary temperature perturbations are indistinguishable from the standard temperature perturbations linearly coming from primordial curvature perturbations and hence should be subdominant compared to the standard ones. We show that small-scale higher order correlation functions (connected non-Gaussian and disconnected Gaussian parts) of primordial curvature perturbations can be probed by investigating auto power spectrum of the generated secondary perturbations and the cross power spectrum with the standard perturbations. This is simply because these power spectra come from higher order correlation functions of primordial curvature perturbations with non-linear parameters such as $f_{\rm NL}$ and $τ_{\rm NL}$ since secondary temperature perturbations are second order effects. Thus, the observational results $l(l+1)C^{TT}_l\simeq 6\times 10^{-10}$ at large scales give a robust and universal upper bound on small-scale non-Gaussianities of primordial curvature perturbations.