Power spectrum constraints from spectral distortions in the cosmic microwave background

Using recent experimental limits on chemical potential distortions from COBE FIRAS, and the large lever-arm spanning the damping of sub- Jeans scale fluctuations to the COBE DMR fluctuations, 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 fluctuation growth and damping as well as thermalization processes. Assuming conservatively that μ < 1.76 x 10^-4^, we find that the 95% upper limit on n is only weakly dependent on other cosmological parameters, e.g., n < 1.60 (h = 0.5) and n < 1.63 (h = 1.0) for {OMEGA}_0_ = 1, with marginally weaker constraints for {OMEGA}_0_ < 1 in a flat model with a cosmological constant.