Future Parameter Constraints from Weak Lensing CMB and Galaxy Lensing Power- and Bispectra

TL;DR

This paper forecasts how future weak lensing surveys can use power spectra and bispectra from CMB and galaxy data to improve cosmological parameter constraints, especially on neutrino mass.

Contribution

It demonstrates the significant potential of weak lensing bispectra, including cross-correlations, to enhance parameter constraints beyond traditional power spectrum analysis.

Findings

Bispectra are detectable at high signal-to-noise in future surveys.

Weak priors allow bispectra to break degeneracies and improve constraints.

Combining CMB and galaxy lensing yields tighter cosmological parameter bounds.

Abstract

Upcoming stage 4 surveys, such as the Simons Observatory, LSST, and Euclid, are poised to measure weak gravitational lensing of the Cosmic Microwave Background (CMB) and galaxies with unprecedented precision. While the power spectrum is the standard statistic used to analyze weak lensing data, non-Gaussianity from non-linear structure growth encodes additional cosmological information in higher-order statistics. We forecast the ability of future surveys to constrain cosmological parameters using the weak lensing power spectrum and bispectrum from both CMB and galaxy surveys, including their cross-correlations. We consider an eight-parameter model ($\Lambda$CDM + $\sum m_\nu$ + $w_0$) and assess constraints for stage 4 survey specifications. In the absence of systematics, both the CMB and galaxy lensing bispectra are found to be detectable at high signal-to-noise. We test two priors: a ''strong'' one based on constraints from CMB temperature and $E$-mode polarization anisotropies, and a ''weak'' one with minimal assumptions. With the weak prior, the bispectrum significantly improves parameter constraints by breaking degeneracies. For strong priors, improvements are more limited, especially for the CMB bispectrum. On small scales, where non-linear effects dominate, the bispectrum's constraining power can rival that of the power spectrum. We also find strong synergy between CMB and galaxy lensing; combining both probes leads to tighter constraints, particularly on neutrino mass. It was recently found that the CMB lensing bispectrum is strongly affected by the Born approximation, so we also consider post-Born corrections but find that our main conclusions remain the same. These results highlight the potential of higher-order lensing statistics and motivate further work on neglected effects such as non-Gaussian covariance, instrumental systematics, and baryonic feedback.