We examine bounds on adiabatic and isocurvature density fluctuations from $mu$-type spectral distortions of the cosmic microwave background (CMB). Studies of such distortion are complementary to CMB measurements of the spectral index and its running, and will help to constrain these parameters on significantly smaller scales. We show that a detection on the order of $mu sim 10^{-7}$ would strongly be at odds with the standard cosmological model of a nearly scale-invariant spectrum of adiabatic perturbations. Further, we find that given the current CMB constraints on the isocurvature mode amplitude, a nearly scale-invariant isocurvature mode (common in many curvaton models) cannot produce significant $mu$-distortion. Finally, we show that future experiments will strongly constrain the amplitude of the isocurvature modes with a highly blue spectrum as predicted by certain axion models.
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