Mitigating foreground bias to the CMB lensing power spectrum for a CMB-HD survey

A promising way to measure the distribution of matter on small scales (k ??? 10 h Mpc???1) is to use gravitational lensing of the cosmic microwave background (CMB). CMB-HD, a proposed high-resolution, low-noise millimeter survey over half the sky, can measure the CMB lensing auto spectrum on such small scales enabling measurements that can distinguish between a cold dark matter (CDM) model and alternative models designed to solve problems with CDM on small scales. However, extragalactic foregrounds can bias the CMB lensing auto spectrum if left untreated. We present a foreground mitigation strategy that provides a path to reduce the bias from two of the most dominant foregrounds, the thermal Sunyaev-Zel???dovich effect and the cosmic infrared background. Given the level of realism included in our analysis, we find that the thermal Sunyaev-Zel???dovich alone and the cosmic infrared background alone bias the lensing auto spectrum by 0.6u and 1.1u, respectively, in the lensing multipole range of L ??? 1/25000; 20000] for a CMB-HD survey; combined these foregrounds yield a bias of only 1.3u. Including these foregrounds, we also find that a CMB-HD survey can distinguish between a CDM model and a 10???22 eV fuzzy dark matter model at the 5u level. These results provide an important step in demonstrating that foreground contamination can be sufficiently reduced to enable a robust measurement of the smallscale matter power spectrum with CMB-HD.