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

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.

💡 Research Summary

This paper investigates possible deviations from General Relativity (GR) on cosmological scales by employing a phenomenological μ‑Σ modified‑gravity (MG) parameterization. In this framework, μ(a) rescales the effective Newtonian constant felt by non‑relativistic matter (affecting clustering), while Σ(a) rescales the Weyl potential that governs light propagation and thus gravitational lensing. The authors adopt a simple time‑dependence proportional to the dark‑energy density, μ(a)=1+μ₀ Ω_DE(a)/Ω_Λ and Σ(a)=1+Σ₀ Ω_DE(a)/Ω_Λ, so that μ₀=Σ₀=0 corresponds to GR. Two background cosmologies are considered: a standard ΛCDM model (w = −1) and a w₀w_a CDM model with a Chevallier‑Polarski‑Linder parametrization for a dynamical dark‑energy equation of state.

The analysis combines several state‑of‑the‑art data sets: (i) KiDS‑Legacy weak‑lensing measurements covering 1347 deg² with tomographic information up to z≈2, featuring improved redshift calibration and shape measurement that boost the constraining power on S₈ by ~30 %; (ii) CMB temperature and polarization spectra from Planck 2018 (restricted to ℓ<1000 for TT and ℓ<600 for TE/EE to avoid double‑counting) together with high‑ℓ data from ACT DR6 and SPT‑3G; (iii) a joint CMB lensing power spectrum reconstructed from Planck PR4, ACT DR6, and SPT‑3G; (iv) BAO distance measurements from DESI DR2; and (v) the DES‑Do vekie super‑nova compilation, a re‑calibrated set of 1820 SNe Ia. The authors use the Cobaya sampler interfaced with MGCAMB to compute theoretical predictions for each model and perform Markov Chain Monte Carlo (MCMC) analyses, checking convergence with the Gelman‑Rubin statistic (R−1 < 0.02).

Four model‑data combinations are explored: ΛCDM, w₀w_a CDM, μ₀Σ₀ ΛCDM, and μ₀Σ₀ w₀w_a, each with various subsets of the data (CMB only, CMB without lensing, CMB+DESI+DES‑Do vekie, and the full combination including KiDS‑Legacy). The key results are summarized in Table I of the paper. For the μ₀Σ₀ ΛCDM case with the full data set, the matter‑clustering parameter is μ₀ = 0.21 ± 0.21, fully consistent with GR (μ₀ = 0). In contrast, the lensing parameter is Σ₀ = 0.149 ± 0.051, representing a 3.0 σ deviation from the GR value Σ₀ = 0. This tension is driven primarily by the large‑scale CMB lensing signal contributed by ACT and SPT, as illustrated in Figure 3 of the paper. When the CMB lensing information is omitted (the “CMB‑nl” case), the Σ₀ constraint weakens dramatically, confirming that the deviation hinges on the lensing data.

Including KiDS‑Legacy improves the precision on Σ₀ by roughly 60 % and on μ₀ by about 43 % relative to CMB‑only constraints, demonstrating the synergistic power of low‑redshift galaxy weak lensing and high‑precision CMB measurements. The authors also test the robustness of the result against a dynamical dark‑energy background (μ₀Σ₀ w₀w_a). Although the central values shift slightly, the Σ₀ deviation remains at the ~2.5–3 σ level, while μ₀ stays consistent with zero. Small anti‑correlations appear between μ₀ and the dark‑energy parameters w₀, w_a, reflecting the known degeneracies between growth and expansion histories.

Potential systematic origins are discussed. The authors note the well‑known “A_lens” anomaly in Planck data, possible residual shear‑calibration biases in KiDS, and uncertainties in photometric redshift distributions. They argue that none of these effects can fully account for the observed Σ₀ excess given the current error budgets, but they caution that future data releases with improved systematics control will be essential to confirm the signal.

The paper concludes that the data reveal a striking pattern: the clustering sector (μ) remains GR‑consistent, while the lensing sector (Σ) shows a statistically significant excess. This could hint at modified‑gravity theories where the effective gravitational coupling for photons differs from that for massive particles (e.g., certain scalar‑tensor models with non‑minimal photon coupling) or could point to unmodeled systematics in the large‑scale CMB lensing reconstruction. The authors emphasize that the combination of high‑resolution CMB experiments (ACT, SPT) with deep weak‑lensing surveys (KiDS‑Legacy) provides a powerful avenue for future precision tests of GR on cosmological scales.