The dissipation of small-scale perturbations in the early universe produces a distortion in the blackbody spectrum of cosmic microwave background photons. In this work, we propose to use these distortions as a probe of the microphysics of dark matter on scales $1\,\textrm{ Mpc}^{ -1}\lesssim k \lesssim 10^{ 4}\,\textrm{ Mpc}^{ -1}$. We consider in particular models in which the dark matter is kinetically coupled to either neutrinos or photons until shortly before recombination, and compute the photon heating rate and the resultant $\mu$-distortion in both cases. We show that the $\mu$-parameter is generally enhanced relative to $\Lambda$CDM for interactions with neutrinos, and may be either enhanced or suppressed in the case of interactions with photons. The deviations from the $\Lambda$CDM signal are potentially within the sensitivity reach of a PRISM-like experiment if $\sigma_{ \textrm{ DM}-\gamma} \gtrsim 1.1\times10^{ -30} \left(m_{ \textrm{ DM}}/\textrm{ GeV}\right) \textrm{ cm}^{ 2}$ and $\sigma_{ \textrm{ DM}-\nu} \gtrsim 4.8\times 10^{ -32} \left(m_{ \textrm{ DM}}/\textrm{ GeV}\right) \textrm{ cm}^{ 2}$ for time-independent cross sections, and $\sigma^{ 0}_{ \textrm{ DM}-\gamma} \gtrsim 1.8 \times 10^{ -40} \left(m_{ \textrm{ DM}}/\textrm{ GeV}\right) \textrm{ cm}^{ 2}$ and $\sigma^{ 0}_{ \textrm{ DM}-\nu} \gtrsim 2.5 \times 10^{ -47} \left(m_{ \textrm{ DM}}/\textrm{ GeV}\right) \textrm{ cm}^{ 2}$ for cross sections scaling as temperature squared, coinciding with the parameter regions in which late kinetic decoupling may serve as a solution to the small-scale crisis. Furthermore, these $\mu$-distortion signals differ from those of warm dark matter (no deviation from $\Lambda$CDM) and a suppressed primordial power spectrum (strongly suppressed or a negative $\mu$-parameter), demonstrating that CMB spectral distortion can potentially be used to distinguish between solutions to the small-scale crisis.
Categories: astro-ph.CO hep-ph