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Evidence for a 3.0$σ$ Deviation in Gravitational Light Deflection from General Relativity at Cosmological Scales with KiDS-Legacy and CMB Lensing

Guo-Hong Du, Tian-Nuo Li, Tonghua Liu, Jing-Fei Zhang, Xin Zhang

TL;DR

This study tests General Relativity at cosmological scales using a phenomenological $μ$-$Σ$ gravity framework, combining KiDS-Legacy weak lensing with joint CMB data (Planck, ACT, SPT), DESI DR2 BAO, and DES-Dovekie supernovae. The analysis explores both $Λ$CDM and $w_0 w_a$CDM background evolutions and employs a late-time, scale-independent parameterization for deviations in matter clustering ($μ_0$) and light deflection ($Σ_0$). Results show $μ_0$ is consistent with GR across data combinations, while $Σ_0$ exhibits a notable deviation up to $3σ$, primarily driven by large-scale CMB lensing points, with KiDS-Legacy data significantly tightening constraints. The work highlights the crucial role of combining high-precision CMB lensing with weak lensing to test gravity on cosmological scales and discusses whether the $Σ_0$ deviation signals new physics or data systematics, outlining future avenues with Euclid and LSST.

Abstract

General Relativity (GR) faces challenges from cosmic acceleration and observational tensions, necessitating stringent tests at cosmological scales. In this work, we probe GR deviations via a $μ$-$Σ$ modified gravity parameterization, integrating KiDS-Legacy weak lensing (1347 deg$^2$, $z\leq 2.0$), joint CMB data (Planck/ACT/SPT), DESI DR2 BAO, and DES-Dovekie supernovae. KiDS-Legacy significantly improves constraint precision: $μ_0$ (matter clustering) by $\sim 43\%$ and $Σ_0$ (gravitational light deflection) by $\sim 60\%$ relative to CMB alone. In the $Λ$CDM background, $μ_0 = 0.21\pm 0.21$ is consistent with GR, while $Σ_0 = 0.149\pm 0.051$ deviates from GR at the 3.0$σ$ level -- attributed to large-scale CMB lensing from ACT/SPT. This precise separation of GR-consistent matter clustering and deviant light deflection provides key observational clues for new physics or data systematics. Our work underscores the critical role of synergizing high-precision CMB and WL data in advancing GR tests.

Evidence for a 3.0$σ$ Deviation in Gravitational Light Deflection from General Relativity at Cosmological Scales with KiDS-Legacy and CMB Lensing

TL;DR

This study tests General Relativity at cosmological scales using a phenomenological - gravity framework, combining KiDS-Legacy weak lensing with joint CMB data (Planck, ACT, SPT), DESI DR2 BAO, and DES-Dovekie supernovae. The analysis explores both CDM and CDM background evolutions and employs a late-time, scale-independent parameterization for deviations in matter clustering () and light deflection (). Results show is consistent with GR across data combinations, while exhibits a notable deviation up to , primarily driven by large-scale CMB lensing points, with KiDS-Legacy data significantly tightening constraints. The work highlights the crucial role of combining high-precision CMB lensing with weak lensing to test gravity on cosmological scales and discusses whether the deviation signals new physics or data systematics, outlining future avenues with Euclid and LSST.

Abstract

General Relativity (GR) faces challenges from cosmic acceleration and observational tensions, necessitating stringent tests at cosmological scales. In this work, we probe GR deviations via a - modified gravity parameterization, integrating KiDS-Legacy weak lensing (1347 deg, ), joint CMB data (Planck/ACT/SPT), DESI DR2 BAO, and DES-Dovekie supernovae. KiDS-Legacy significantly improves constraint precision: (matter clustering) by and (gravitational light deflection) by relative to CMB alone. In the CDM background, is consistent with GR, while deviates from GR at the 3.0 level -- attributed to large-scale CMB lensing from ACT/SPT. This precise separation of GR-consistent matter clustering and deviant light deflection provides key observational clues for new physics or data systematics. Our work underscores the critical role of synergizing high-precision CMB and WL data in advancing GR tests.
Paper Structure (4 sections, 6 equations, 3 figures, 2 tables)

This paper contains 4 sections, 6 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Results and discussions
  4. Conclusion

Figures (3)

  • Figure 1: The $1\sigma$ and $2\sigma$ credible-interval contours for the $\mu_0$ and $\Sigma_0$ parameters, utilizing the CMB, DESI, DES-Dovekie, and KiDS-Legacy data. The results for the $\mu_0 \Sigma_0 \Lambda\mathrm{CDM}$ and $\mu_0 \Sigma_0 w_0 w_a$ models are displayed in the left and right panels, respectively.
  • Figure 2: Whisker plots for the $\mu_0$ and $\Sigma_0$ parameters using the CMB, DESI, DES-Dovekie, and KiDS-Legacy data. The results for the $\mu_0 \Sigma_0 \Lambda\mathrm{CDM}$ and $\mu_0 \Sigma_0 w_0 w_a$ models are represented by circles and squares, respectively.
  • Figure 3: The CMB lensing potential power spectrum (upper panel) and fractional residuals relative to the best-fit $\Lambda$CDM model (lower panel). The black squares with error bars represent the joint lensing data points, plotted alongside the individual bandpowers from Planck PR4 (light yellow), ACT DR6 (light red), and SPT-3G M2PM (light blue) shown as semi-transparent error boxes. Theoretical curves are displayed using the results from CMB+DESI+DES-Dovekie+KiDS-Legacy for the $\Lambda$CDM (solid gray), $w_0w_a$CDM (dotted pink), $\mu_0\Sigma_0\Lambda$CDM (dashed blue), and $\mu_0\Sigma_0 w_0w_a$ (dash-dotted orange) models.