Parameter constraints from cross-correlation of CMB lensing with galaxy clustering

The lensing convergence measurable with future CMB surveys like CMB-S4 will be highly correlated with the clustering observed by deep photometric large scale structure (LSS) surveys such as the LSST, with cross-correlation coefficient as high as 95\%. This will enable use of sample variance cancellation techniques to determine cosmological parameters, and use of cross-correlation measurements to break parameter degeneracies. Assuming large sky overlap between CMB-S4 and LSST, we show that a joint analysis of CMB-S4 lensing and LSST clustering can yield very tight constraints on the matter amplitude $\sigma_8(z)$, halo bias, and $f_\mathrm{NL}$, competitive with the best stage IV experiment predictions, but using complementary methods, which may carry different and possibly lower systematics. Having no sky overlap between experiments degrades the precision of $\sigma_8(z)$ by a factor of 20, and that of $f_\mathrm{NL}$ by a factor of 1.5 to 2. Without CMB lensing, the precision always degrades by an order of magnitude or more, showing that a joint analysis is critical. Our results also suggest that CMB lensing in combination with LSS photometric surveys is a competitive probe of the evolution of structure in the redshift range $z\simeq 1-7$, probing a regime that is not well tested observationally. We explore predictions against other surveys and experiment configurations, finding that wide patches with maximal sky overlap between CMB and LSS surveys are most powerful for $\sigma_8(z)$ and $f_\mathrm{NL}$.