Towards testing gravity with LSST using $E_G$

TL;DR

This work analyzes the potential of using the E_G statistic to test General Relativity with LSST weak lensing and DESI galaxy clustering, accounting for uncertainties in the present-day matter density $\Omega_M^0$. It develops a comprehensive covariance framework combining analytic and simulation-based methods, and assesses the impact of nonlinear galaxy bias on $E_G$ and its calibration via a nonlinear-bias correction factor $C_b(r_p)$. The authors implement a posterior predictive test to incorporate $\Omega_M^0$ uncertainty and demonstrate that the prior on $\Omega_M^0$ is the dominant factor determining the power to reject GR under MG scenarios, with Planck-like priors yielding substantially higher rejection rates than Stage III priors. Their results suggest that, for a robust gravity test with LSST+DESI, precise external constraints on $\Omega_M^0$ are crucial, and that nonlinear bias corrections are essential to maximize the usable scales. Overall, the paper provides a practical, model-agnostic approach to gravity tests with next-generation surveys and highlights the critical role of priors in interpreting $E_G$ measurements.

Abstract

$E_G$ is a summary statistic that combines cosmological observables to achieve a test of gravity that is relatively model-independent. Here, we consider the power of a measurement of $E_G$ using galaxy-galaxy lensing and galaxy clustering with sources from the Rubin Observatory's Legacy Survey of Space and Time (LSST), and lenses from the Dark Energy Spectroscopic Instrument (DESI). We first update the theoretical framework for the covariance of $E_G$ to accommodate this Stage IV scenario. We then demonstrate that $E_G$ offers in principle a model-agnostic test of gravity using only linear-scale information, with the caveat that a careful treatment of galaxy bias is required. We finally address the persistent issue of $E_G$'s theoretical dependence on the measured value of $Ω_{\rm M}^0$. We propose a framework that takes advantage of the posterior predictive test to consistently incorporate uncertainty on $Ω_{\rm M}^0$ in tests of gravity with $E_G$, which should be of general use beyond the LSST+DESI scenario. Our forecasting study using this method shows that the prior information available for $Ω_{\rm M}^0$ is instrumental in determining the power of $E_G$ in the LSST+DESI context. For the full survey dataset, with priors on $Ω_{\rm M}^0$ from existing CMB data, we find that for some modified gravity scenarios considered, we are likely to be able to reject the GR null hypothesis.

Figures (11)

• Figure 1: Left: Redshift distribution of DESI LRG sample, data points from zhou2023target. Right: Redshift distribution of LSST Year 1 and LSST Year 10 source sample. Numerical values of $\frac{dN}{dz}$ reflect in all cases the fact that distributions are normalised to unity.
• Figure 2: Correlation matrices of the constituent probes of $E_G$. Within the $\Upsilon_{gm}(r_p)$ and $\Upsilon_{gg}(r_p)$ sub-blocks, bins increase logarithmically in $r_p$ with bin centres ranging from 1.4 to 87.9 Mpc/h.
• Figure 3: Correlation matrices of $E_G(r_p)$. Bins increase logarithmically in $r_p$ with bin centres ranging from 1.4 to 87.9 Mpc/h.
• Figure 4: Illustration of which points are kept in the linear-only scale cuts scenario for $\Upsilon_{gm}$ (top), $\Upsilon_{gg}$ (middle) and $E_G$ (bottom), assuming a linear galaxy bias. The points plotted are for the fiducial data vector with non-linear modelling from halofit (but linear galaxy bias), with LSST Year 1 sources. The $r_p$ bins kept vs discarded are the same in both the LSST Year 1 and Year 10 source cases.
• Figure 5: Illustration of which points are kept in the linear-only scale cuts scenario for $\Upsilon_{gm}$ (top), $\Upsilon_{gg}$ (middle) and $E_G$ (bottom), assuming a nonlinear galaxy bias as described in Section \ref{['subsec:scaledepbias']}. The data vector plotted assumes this nonlinear galaxy bias model. We display the case with LSST Year 1 source galaxies; for LSST Year 10 sources, we would discard one additional point in the $E_G$ case, at $r_p \approx 30$ Mpc/h.