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

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 ($Λ$CDM + $\sum m_ν$ + $w_0$) 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.

Figures (13)

• Figure 1: Our galaxy redshift distribution (\ref{['eq:galzdist']}) split up into 4 bins. The dashed lines correspond to the actual distributions of the bins after taking into account galaxy redshift uncertainty. We assumed no galaxy bias in the redshift estimation and a Gaussian error given by $\sigma_z = 0.05 (1+z)$. This is representative of EUCLID level of redshift uncertainty EuclidSciRD.
• Figure 2: CMB (right) and galaxy (left) lensing potential power spectra compared to associated experimental noise. Current (stage 3) noise values are displayed as well as near future (some of the stage 4 experiments are already in operation, but expected noise levels are only achieved after several years of integration) (stage 4) noise values. The CMB lensing experiment uses only polarization. CMB noise values are chosen in accordance with Namikawa_2016. For comparison we also show the reconstruction noise for the Simons Observatory Ade2019. Shear noise values are chosen to be similar to e.g. EUCLID measurements laureijs2009 for stage 4 and e.g. KiDS kuijken2021 for stage 3. Because we have 4 bins the galaxy density is a 4th of the total galaxy density.
• Figure 3: Signal-to-noise ratios for galaxy lensing (left) and CMB lensing (right) bispectra for stage 3 (dashed) and stage 4 (not dashed) surveys as a function of maximum multipole measured. The minimum multipole is always $l_{\text{min}}=2$. The multipole range used for CMB lensing reconstruction is $2\leq \ell \leq 10^4$. Using a more conservative range such as $30\leq \ell \leq 5000$ used to calculate Simons Observatory noise curves do not significantly affect the results.
• Figure 4: Parameter constraints and confidence ellipses for $\mu_\nu$, $w_0$, $\sigma_8$, and $\Omega_m$. Using "stage 4" noise with multipole range from $2$ to $2000$. The colored plots show CMB lensing power and/or bispectrum constraints. We use the weak priors listed in table \ref{['tab:fiducialpars']}. The confidence ellipses are for $1\sigma$ certainty. They show approximate degeneracies in the information gained from a survey if they are "stretched". When the information of ellipses with degeneracies in different directions is combined, the degeneracies are removed and the constraints typically become much better on the relevant parameters. The black plots show the constraints using all lensing information, i.e. CMB lensing spectra, galaxy lensing spectra, and all cross spectra.
• Figure 5: Same as figure \ref{['fig:paramconstraintstightcmb']}, except we use the CMB temperature and polarization based priors listed in table \ref{['tab:fiducialpars']}.