Power Spectrum Constraints from Spectral Distortions in the Cosmic Microwave Background

Using recent experimental limits on distortions from COBE FIRAS, and the large lever-arm spanning the damping of sub-Jeans scale uctuations to the scale of the COBE DMR uctuations, we set a constraint on the slope of the primordial power spectrum n. It is possible to analytically calculate the contribution over the full range of scales and redshifts, correctly taking into account uctuation growth and damping as well as thermalization processes. We nd that the 95% upper limit is weakly dependent on cosmological parameters, e.g., n < 1:54 (h = 0:5) and n < 1:56 (h = 1:0) for 0 = 1 with marginally weaker constraints for 0 < 1 in a at 0 + = 1 universe.