Cross Correlating Cosmological Probes for LSST & CMB-S4
The upcoming years will be populated with state-of-the-art Stage-IV cosmological surveys. This paper forecasts the cosmological information we expect to constrain using probes from the Rubin Observatory Legacy Survey of Space and Time (LSST) and CMB-S4. We explore the effectiveness of different large-scale-structure probes, including the power spectra of galaxy weak lensing, galaxy position, Cosmic Microwave Background (CMB) lensing, and their cross-correlations. We use correlated lognormal simulations with the expected redshift distributions, galaxy number densities, and noise levels of the LSST survey. For CMB weak lensing, we use CMB-S4 lensing simulations with anticipated noise levels to obtain the expected error bars of each probe. We investigate the constraining power of the cosmological parameters for the individual probes and their combinations in an idealized scenario. We do not take into account astrophysical and observational parameters such as galaxy bias variations and photometric redshift un- certainties. Overall, we find the auto-correlated probes hold stronger constraints on cosmological parameters than the cross-correlated probes due to kernel differences. However, the cross-correlation of galaxy clustering and CMB lensing is very comparable to the auto-correlation of galaxy clustering with only an 8% stronger constraint in S8. It will be important for future surveys to use these auto and cross probes in combination due to the different astrophysical and systematic effects involved in CMB and late-time galaxy data. When systematics are added to this analysis, the cross probes will serve as a check for systematic biases in individual probes. In addition, we find a significant increase in constraint using all four probes in combination. This can be illustrated by the increase in constraint of S8 by 93.2% comparing galaxy clustering auto-correlation to a combination of all probes. Our study is a first step toward forecasting the high-precision cosmological constraints we expect to obtain using the next generation of large-scale structure probes.