Measurement of the Weyl Potential Evolution and $E_G$ Statistic from KiDS-1000, BOSS and 2dFLenS

Abstract

A recently developed model-independent approach to measuring the Weyl potential has shown some tensions with $\Lambda$CDM (Lambda Cold Dark Matter) in DES (Dark Energy Survey) Y3 data. We apply this framework to Kilo-Degree Survey (KiDS-1000) weak lensing and BOSS/2dFLenS galaxy clustering using the KiDS Cosmology Analysis Pipeline (KCAP) in two redshift bins. To apply this method to the BOSS spectroscopic wedges, we take the early-time power spectrum from a redshift where General Relativity (GR) is recovered and jointly fit the late-time observables $\hat{b}$, $\hat{f}$, and $\hat{J}$. With Planck18 priors, the CMASS measurement of $\hat{J}$ is $1.50\sigma$ below the GR prediction, while the LOWZ measurement remains consistent with it. The decrease in the central value of $\hat{J}$ from LOWZ to CMASS provides a mild indication of the previously reported ``Lensing is low'' behavior. Without Planck18 priors, we obtain $E_G(0.38)=0.503\pm0.054$ and $E_G(0.61)=0.444\pm0.054$, both consistent with GR. Furthermore, phenomenological gravity tests also show no significant preference for modified gravity.