[Paper Review] Can CMB Lensing Help Cosmic Shear Surveys?

Sudeep Das, Josquin Errard+1 more|arXiv (Cornell University)|Nov 10, 2013

Particle physics theoretical and experimental studiesPhysics and Astronomy20 citations

TL;DR

This paper proposes using cross-correlations between cosmic microwave background (CMB) lensing, optical cosmic shear, and spectroscopic galaxy surveys to calibrate shear multiplicative bias—a major systematic in weak lensing surveys. By combining these cross-correlations, the method reduces multiplicative bias uncertainty to 0.5% in high-redshift bins and improves cosmological constraints by 20–25%, significantly enhancing dark energy and neutrino mass measurements from upcoming surveys like HSC and LSST.

ABSTRACT

Yes! Upcoming galaxy shear surveys have the potential to significantly improve our understanding of dark energy and neutrino mass if lensing systematics can be sufficiently controlled. The cross-correlations between the weak lensing shear, galaxy number counts from a galaxy redshift survey, and the CMB lensing convergence can be used to calibrate the shear multiplicative bias, one of the most challenging systematics in lensing surveys. These cross-correlations can significantly reduce the deleterious effects of the uncertainties in multiplicative bias.

Motivation & Objective

• Address the challenge of multiplicative bias in optical cosmic shear surveys, a key systematic limiting cosmological parameter constraints.
• Overcome the degeneracy between redshift-dependent multiplicative bias and non-standard growth of structure, which can bias dark energy and neutrino mass measurements.
• Improve constraints on cosmological parameters by leveraging cross-correlations between CMB lensing, optical shear, and spectroscopic galaxy tracers.
• Demonstrate that combining CMB lensing with spectroscopic surveys breaks degeneracies unresolvable by lensing correlations alone.
• Enable tighter constraints on dark energy, neutrino mass, and deviations from general relativity using upcoming weak lensing surveys.

Proposed method

• Use the Limber approximation and spherical harmonic decomposition to model the cross-correlation power spectra between CMB lensing convergence (κ_CMB), optical shear (κ_opt), and galaxy number counts (Σ).
• Formulate the cross-correlation power spectra Cℓ^κ_CMBΣ and Cℓ^κ_optΣ, where the latter includes the multiplicative bias m as a free parameter.
• Apply Fisher matrix analysis to forecast constraints on multiplicative bias, galaxy bias, and cosmological parameters using realistic survey configurations.
• Incorporate cross-correlations between CMB lensing, optical shear, and spectroscopic galaxy surveys to break degeneracies between multiplicative bias and growth rate.
• Use the CMB lensing estimator as a robust, bias-free tracer of the projected matter overdensity to calibrate the shear multiplicative bias.
• Assess the impact of adding spectroscopic galaxy data (e.g., BOSS-like) to CMB and optical lensing cross-correlations to improve bias and cosmological parameter constraints.

Experimental results

Research questions

• RQ1 Can CMB lensing cross-correlations with optical shear and spectroscopic galaxy surveys effectively calibrate the redshift-dependent multiplicative bias in cosmic shear surveys?
• RQ2 To what extent can cross-correlations between CMB lensing, optical shear, and spectroscopic tracers break the degeneracy between multiplicative bias and non-standard growth of structure?
• RQ3 How much do cosmological parameter constraints improve when multiplicative bias is calibrated via multi-probe cross-correlations compared to using lensing correlations alone?
• RQ4 What level of multiplicative bias uncertainty can be achieved using CMB lensing and spectroscopic surveys for upcoming surveys like HSC and LSST?
• RQ5 Can the inclusion of spectroscopic data significantly reduce the uncertainty in galaxy bias parameters, thereby improving cosmological constraints?

Key findings

• The combination of CMB lensing, optical shear, and spectroscopic galaxy surveys reduces the uncertainty in the shear multiplicative bias to 0.5% in the highest redshift bin, significantly improving calibration.
• Fisher analysis shows that adding spectroscopic galaxy data reduces multiplicative bias uncertainty from ~6% to 0.5% in the highest redshift bin, with the most significant improvement in the highest-redshift bin.
• Cosmological parameter constraints improve by 20–25% when multiplicative bias is calibrated via cross-correlations, with the largest gains in σ8 and neutrino mass sum (Σmν).
• For the HSC survey, combining CMB lensing from an ACTPol-like experiment with BOSS-like spectroscopy enables multiplicative bias calibration at the 0.5–2.0% level.
• Stage-III CMB experiments could calibrate LSST-like optical shear surveys at the 0.25% level, enabling sub-percent bias control.
• The inclusion of cross-correlations between CMB lensing, optical shear, and galaxy tracers reduces the marginalized error on σ8 from 0.0211 to 0.0158 (with bias fixed) and from 0.0238 to 0.0199 (with bias varying), demonstrating robust improvement.