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In the early Universe, energy stored in small-scale density perturbations isquickly dissipated by Silk-damping, a process that inevitably generates mu- andy-type spectral distortions of the cosmic microwave background (CMB). Thesespectral distortions depend on the shape and amplitude of the primordial powerspectrum at wavenumbers k < 10^4 Mpc^{-1}. Here we study constraints on theprimordial power spectrum derived from COBE/FIRAS and forecasted for PIXIE. Weshow that measurements of mu and y impose strong bounds on the integratedsmall-scale power, and we demonstrate how to compute these constraints usingk-space window functions that account for the effects of thermalization anddissipation physics. We show that COBE/FIRAS places a robust upper limit on theamplitude of the small-scale power spectrum. This limit is about three ordersof magnitude stronger than the one derived from primordial black holes in thesame scale range. Furthermore, this limit could be improved by another threeorders of magnitude with PIXIE, potentially opening up a new window to earlyUniverse physics. To illustrate the power of these constraints, we considerseveral generic models for the small-scale power spectrum predicted bydifferent inflation scenarios, including running-mass inflation models andinflation scenarios with episodes of particle production. PIXIE could placevery tight constraints on these scenarios, potentially even ruling outrunning-mass inflation models if no distortion is detected. We also show thatinflation models with sub-Planckian field excursion that generate detectabletensor perturbations should simultaneously produce a large CMB spectraldistortion, a link that could potentially be established by PIXIE.

Probing the inflaton: Small-scale power spectrum constraints from measurements of the CMB energy spectrum