  The small-scale crisis, discrepancies between observations and N-body
simulations, may imply suppressed matter fluctuations on subgalactic distance
scales. Such a suppression could be caused by some early-universe mechanism
(e.g., broken scale invariance during inflation), leading to a modification of
the primordial power spectrum at the onset of the radiation-domination era.
Alternatively, it may be due to nontrivial dark-matter properties (e.g., new
dark-matter interactions or warm dark matter) that affect the matter power
spectrum at late times, during radiation domination, after the perturbations
re-enter the horizon. We show that early- and late-time suppression mechanisms
can be distinguished by measurement of the $\mu$ distortion to the frequency
spectrum of the cosmic microwave background. This is because the $\mu$
distortion is suppressed, if the power suppression is primordial, relative to
the value expected from the dissipation of standard nearly scale-invariant
fluctuations. We emphasize that the standard prediction of the $\mu$ distortion
remains unchanged in late-time scenarios even if the dark-matter effects occur
before or during the era (redshifts $5\times 10^4 \lesssim z \lesssim 2\times
10^6$) at which $\mu$ distortions are generated.
