CMB-HD as a Probe of Dark Matter on Sub-Galactic Scales

We show for the first time that high-resolution CMB lensing observations can probe structure on sub-galactic scales. In particular, a CMB-HD experiment can probe out to k ~ 55 h/Mpc, corresponding to halo masses of about $10^8 M_{\odot}$. Over the range 0.005 h/Mpc < k < 55 h/Mpc, spanning four orders of magnitude, the total lensing signal-to-noise ratio (SNR) from the temperature, polarization, and lensing power spectra is greater than 1900. CMB-HD gains most of the lensing SNR at small scales from the temperature power spectrum, as opposed to the lensing spectrum. These lensing measurements allow CMB-HD to distinguish between cold dark matter (CDM) and non-CDM models that change the matter power spectrum on sub-galactic scales. We also find that CMB-HD can distinguish between baryonic feedback effects and non-CDM models due to the different way each impacts the lensing signal. The kinetic Sunyaev-Zel'dovich (kSZ) power spectrum further constrains non-CDM models that deviate from CDM on the smallest scales CMB-HD measures. For example, CMB-HD can detect 1 keV warm dark matter (WDM) at 30$\sigma$, or rule out about 7 keV WDM at 95% CL, in a $\Lambda$WDM + $N_{\rm{eff}} + \sum m_\nu + m_{\rm{WDM}} + \log_{10}T_{\rm{AGN}} + A_{\rm{kSZ}} + n_{\rm{kSZ}}$ model; here $T_{\rm{AGN}}$ characterizes the strength of the feedback, and $A_{\rm{kSZ}}$ and $n_{\rm{kSZ}}$ allow freedom in the amplitude and slope of the kinetic Sunyaev-Zel'dovich power spectrum. This work provides an initial exploration of what can be achieved with reasonable assumptions about systematic effects. We make the CMB-HD Fisher code used here publicly available, and note that it can be modified to use any non-CDM model that changes the matter power spectrum.