[Paper Review] The Synergy between Weak Lensing and Galaxy Redshift Surveys

Roland de Putter, Olivier Doré+1 more|arXiv (Cornell University)|Aug 28, 2013

Astronomy and Astrophysical Research7 citations

TL;DR

This paper investigates the synergistic potential of combining weak lensing (WL) and spectroscopic galaxy clustering (GC) surveys for constraining dark energy and modified gravity. Using Fisher matrix forecasts for upcoming surveys like SuMIRe, EUCLID, and WFIRST, it demonstrates that WL+GC jointly improve dark energy figure of merit by up to 2.5× compared to either probe alone, with growth rate $f(z)$ constrained at the few percent level when treated as a free function—highlighting strong complementarity despite minimal gains from survey overlap.

ABSTRACT

We study the complementarity of weak lensing (WL) and spectroscopic galaxy clustering (GC) surveys, by forecasting dark energy and modified gravity constraints for three upcoming survey combinations: SuMIRe (Subaru Measurement of Images and Redshifts, the combination of the Hyper Suprime-Cam lensing survey and the Prime Focus Spectrograph redshift survey), EUCLID and WFIRST. From the WL surveys, we take into account both the shear and clustering of the source galaxies and from the GC surveys, we use the three-dimensional clustering of spectroscopic galaxies, including redshift space distortions. A CMB prior is included in all cases. Focusing on the large-scale, two-point function information, we find strong synergy between the two probes. The dark energy figure of merit from WL+GC is up to a factor ~2.5 larger than from either probe alone. Considering modified gravity, if the growth factor f(z) is treated as a free function, it is very poorly constrained by WL or GC alone, but can be measured at the few percent level by the combination of the two. On the other hand, for cosmological constraints derived from (angular) power spectra and considering statistical errors only, it hardly matters whether the surveys overlap on the sky or not. For instance, the dark energy figure of merit for overlapping surveys is at most ~20 % better than in the disjoint case. This modest gain can be traced to the fundamental fact that only a small fraction of the total number of modes sampled by the GC survey (or by the WL survey) contributes to the cross-correlations between WL and GC.

Motivation & Objective

• To quantify the cosmological constraint improvement from combining weak lensing and spectroscopic galaxy clustering surveys.
• To assess whether overlapping sky coverage between WL and GC surveys provides significant statistical advantages over disjoint surveys.
• To evaluate the performance of combined WL+GC in constraining dark energy and modified gravity, particularly the growth rate $f(z)$ as a free function.
• To resolve discrepancies in prior literature regarding 'same-sky' benefits in cross-correlation forecasts.
• To examine the role of two-point statistics (angular spectra and 3D power spectra) in determining synergy strength, under CMB prior and large-scale assumptions.

Proposed method

• Uses Fisher matrix forecasts to project cosmological constraints for three upcoming survey combinations: SuMIRe, EUCLID, and WFIRST.
• Models both cosmic shear (weak lensing) and source galaxy clustering from WL surveys, and 3D galaxy clustering with redshift space distortions from GC surveys.
• Applies the Limber approximation to compute angular power spectra and includes a CMB prior in all forecasts.
• Compares constraints from overlapping vs. disjoint survey areas, focusing on cross-correlations between WL and GC fields.
• Performs sensitivity tests with varying $k_{ ext{max}}$ (0.1–0.2 h/Mpc) to assess non-linear scale modeling effects.
• Reproduces and compares with prior work (e.g., Kirk et al. 2013) to investigate discrepancies in same-sky benefit estimates.

Experimental results

Research questions

• RQ1 How much does combining weak lensing and galaxy redshift surveys improve constraints on dark energy compared to using either probe alone?
• RQ2 To what extent does spatial overlap between WL and GC surveys enhance cosmological constraints beyond simple sky coverage gains?
• RQ3 Can the growth rate of structure $f(z)$ be constrained at the few percent level when treated as a free function using WL+GC data?
• RQ4 Why do some studies report large 'same-sky' benefits (e.g., 3–5× improvement) while others, including this work, find only modest gains (~20%)?
• RQ5 How do different modeling choices—such as the use of angular spectra vs. 3D power spectra and $k_{ ext{max}}$ cutoffs—affect the forecasted synergy?

Key findings

• The dark energy figure of merit from combining weak lensing and galaxy clustering surveys is up to 2.5 times larger than from either probe alone.
• When $f(z)$ is treated as a free function, it is poorly constrained by WL or GC individually but can be measured at the few percent level when both probes are combined.
• The improvement from survey overlap is minimal—at most 20% better figure of merit for overlapping vs. disjoint surveys—due to the small fraction of shared modes contributing to cross-correlations.
• The modest gain from overlap is not due to overly optimistic non-linear scale modeling, as confirmed by repeating forecasts with $k_{ ext{max}} = 0.1~h/\text{Mpc}$, which still shows negligible overlap benefit.
• Discrepancies with prior works (e.g., Kirk et al. 2013) suggesting larger same-sky benefits may stem from differences in modeling assumptions, particularly in angular power spectrum treatment.
• Synergy from small-scale clustering and galaxy-halo connection information (e.g., via cross-correlations of spectroscopic galaxies with photometric or lensing galaxies) is promising but requires overlapping surveys and improved modeling of non-linear physics.