Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

Abstract

We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum–bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

Cross-bispectra constraints on modified gravity theories from the Nancy Grace Roman Space Telescope and the Rubin Observatory Legacy Survey of Space and Time

“…This is consistent with the findings of Ref. [9], where the signal-to-noise ratio of the lensing convergence bispectrum plateaus for n zbin ≥ 5 with or without the non-Gaussian and supersample covariance. Given that the lensing bispectrum is the main beneficiary of tomography, we expect similar conclusions to hold for our combined bispectrum results, and so we do not explore much higher numbers of redshift bins.…”

“…In Ref. [9], it was shown for the lensing power spectrum (which dominates constraints in this study) that including non-Gaussian and supersample covariance could reduce the signal-to-noise ratio of the C κκ l by a factor of 2-3 in the l max ¼ 1000-3000 range without tomography. However, when tomography is used, the reduction becomes less than a factor of 2.…”

“…In Ref. [9], it was shown that including these terms lead to at most a factor of 2-3 degradation in the signal-to-noise for combined lensing power spectrum and bispectrum for the range l max ¼ 1000-3000, which further reduces to a factor of ≲2 when tomography is used. A similar argument as the one made for the power spectrum constraints in Sec.…”

“…Just as using cross-power spectra can break parameter degeneracies leading to improved constraints, we expect a similar effect by cross-correlating probes in the bispectra. Typically the lensing convergence bispectrum and the galaxy bispectrum have been studied individually (e.g., [8][9][10][11]). Here, we combine for the first time the galaxy and lensing convergence auto-bispectra as well as their crossbispectra between these probes in different tomographic bins, to exploit their potential to improve on parameter constraints.…”

Optimal void finders in weak lensing maps

“…The first is Minkowski functionals, which can provide additional constrains on the dark energy equation of state parameter (Kratochvil et al 2012;Petri et al 2013;Ling et al 2015;Marques et al 2019). The WL bispectrum, which is sensitive to non-Gaussianity by definition, has been shown to be a useful statistic for future surveys (Cooray & Hu 2001;Rizzato et al 2019;Munshi & McEwen 2020), and can be used to improve parameter constraints, such as neutrino masses (Coulton et al 2019). And finally, WL minima, local minima in the convergence field, are less sensitive to baryonic effects, and offer certain advantages over WL peaks (Coulton et al 2020).…”