Sample variance cancellation for future spectroscopic surveys

High-redshift spectroscopic galaxy surveys will be the scientific engines of the next generation of large-scale structure cosmology. The clustering signal of high redshift, star-forming Lyman-$α$ emitters (LAEs) will be of key importance for obtaining high-redshift constraints on the growth of structure and redshift-space distortions. The complex radiative transfer (RT) of Lyman-$α$ photons alters the symmetry group respected by the overdensity field constructed from these galaxies, and so the observed large-scale clustering of LAEs may have an angular dependence that differs significantly from that of linear theory, possibly biasing inference of cosmological parameters. While such an effect has been seen in simulations, its amplitude in nature and its detailed form remains unclear. In the restricted context of a linear, Gaussian model, we outline a procedure for pinning down the type and amplitude of such changes in angular dependence on large scales due to unknown RT or a more general unmodeled angular effect in the hypothetical scenario in which an observer is presented with LAE data containing such an effect. We show that if a second tracer without the modified angular dependence is available for cross correlation with the LAEs at the same redshifts (e.g., Lyman-break galaxies), then, with a high redshift survey of modest size, it is possible to rapidly identify: 1) the presence of a nontrivial angular functional form of radiative transfer (by a conditional field-level realization), 2) the functional form itself (with an optimal filter that we derive), and 3) the value of its amplitude with an uncertainty (via an adaptation of the standard quadratic estimator). Such sample-variance-cancellation strategies therefore provide a statistical solution to unknown astrophysical or systematic angular clustering dependence, including from RT.