Testing gravitational physics by combining DESI DR1 and weak lensing datasets using the E_G estimator

TL;DR

This work tests Einstein’s General Relativity on cosmological scales by measuring the gravitational estimator E_G using DESI-DR1 spectroscopic data in combination with KiDS-1000, DES-Y3, and HSC weak-lensing surveys. The authors develop and apply a robust measurement pipeline that combines galaxy–galaxy lensing, projected clustering, and redshift-space distortions, using annular statistics to suppress non-linearities and both direct and maximum-likelihood approaches to extract E_G(z). Their results show E_G is consistent with the scale-independent GR prediction, E_G(z) = $\frac{\Omega_m}{f(z)}$, calibrated by Planck, across a wide redshift range up to z ~ 1, and exhibit no significant scale dependence. The study demonstrates the power of DESI’s redshift leverage and weak-lensing cross-correlations to constrain gravity and lays groundwork for future high-precision tests with upcoming surveys.

Abstract

The action of gravitational physics across space-time creates observable signatures in the behaviour of light and matter. We perform combined-probe studies using data from the Baryon Oscillation Spectroscopic Survey (BOSS) and Dark Energy Spectroscopic Instrument survey Data Release 1 (DESI-DR1), in combination with three existing weak lensing surveys, the Kilo-Degree Survey (KiDS), the Dark Energy Survey (DES), and the Hyper Suprime-Cam Survey (HSC), to test and constrain General Relativity (GR) in the context of the standard model of cosmology (LCDM). We focus on measuring the gravitational estimator statistic, E_G, which describes the relative amplitudes of weak gravitational lensing and galaxy velocities induced by a common set of overdensities. By comparing our amplitude measurements with their predicted scale- and redshift-dependence within the GR+LCDM model, we demonstrate that our results are consistent with the predictions of the Planck cosmology. The redshift span of the DESI dataset allows us to perform these E_G measurements at the highest redshifts achieved to date, z ~ 1.

Figures (9)

• Figure 1: The sky coverage of BOSS-DR12 (top) and DESI-DR1 (bottom), showing the overlapping footprints for KiDS-1000 (red), DES-Y3 (green), HSC-Y1 (light blue) and HSC-Y3 (dark blue), projected onto the celestial sphere using equatorial coordinates (right ascension and declination). Two hemispheres are shown in each case, centred on the North Galactic Pole (NGP) and South Galactic Pole (SGP) regions. The full DESI footprint is shown in the bottom panel as the light grey region.
• Figure 2: The correlation matrix $C_{ij}/\sqrt{C_{ii} C_{jj}}$ corresponding to the covariance matrix $C_{ij} = \text{Cov}[E^{l_i}_G(R_u),E^{l_j}_G(R_v)]$ given in Eq. \ref{['eq:egCovErr']} for the joint analysis of the DESI-DR1 and KiDS-1000 datasets. The $E_G(z,R)$ data vector is arranged looping first over redshift bins, then scale bins for $R > R_0$. The dotted lines in the figure indicate the division into six lens redshift bins.
• Figure 3: This figure displays mean cross-correlation measurements from the Buzzard simulation mock catalogues, assuming $R_0 = 3\, h^{-1}$ Mpc. Each column represents one of the six simulated lens samples. The top row shows $\Upsilon_{gg}(R)$ measurements, the next three rows show $\Upsilon_{gm}(R)$ measurements using these lens samples and the simulated KiDS-1000, DES-Y3 and HSC-Y1 source samples, and the final three rows show the corresponding $E_G(R,z)$ measurements using the direct ratio method. The measurements are compared with the fiducial model prediction depicted by the solid black line, with errors from the diagonal of the covariance matrix. The shaded regions in the $E_G(R,z)$ panels illustrate the 68% confidence region of the fit of the general scale-dependent test model shown in Eq. \ref{['eq:scaleModel']}.
• Figure 4: The determination of the scale-averaged value $E_G(z)$, using the maximum-likelihood method, for each lens redshift bin of the KiDS-1000, DES-Y3 and HSC-Y1 Buzzard simulations for varying non-linear cut-off scales $R_0 = (1, 2, 3, 4) \, h^{-1}$ Mpc. The solid black line represents the fiducial model prediction. The mean of the measurements across the $N_{\rm reg}$ mock regions is plotted, with the error scaled by $1/\sqrt{N_{\rm reg}}$. The fiducial $E_G(z)$ values are recovered with the choice $R_0 = 3\, h^{-1}$ Mpc.
• Figure 5: This figure displays cross-correlation measurements from the BOSS lens catalogues and KiDS-1000, DES-Y3 and HSC-Y1 source samples, displayed in the same style as Fig. \ref{['fig:eg_allBuzzard']}.