Observable detail · COSMOLOGY

S₈

Matter-clustering amplitude — ~2σ tension under canonical constant-\(P_0\) treatment.

Mechanism

Linear growth-of-structure on a \(\Lambda\)CDM background under DCT's perturbation-level programme: \(\delta'' + 2H\delta' - 4\pi G \rho_m P_{\rm eff}\,\delta = 0\). With \(P_{\rm eff} = P_0 = 0.851\) (canonical constant value), the late-time growth is suppressed below the Planck-extrapolated \(\Lambda\)CDM value, giving \(\sigma_8 = 0.756\) and \(S_8 = \sigma_8\sqrt{\Omega_m/0.3} \approx 0.776\). KiDS-Legacy 2025 measures \(0.815 \pm 0.018\) — a \(\sim\!2\sigma\) tension. This is one of the two dominant downward drivers of the calibrated probability band.

Amendment

An earlier interim extension proposed a temporal Avrami \(P(z)\) profile evaluated at the lensing-kernel epoch (where \(P(z) \to 1\) at \(z \approx 0.3\)–0.5), which gave \(S_8^{\rm DCT,Avrami} = 0.811\) at \(0.18\sigma\) from the KiDS-Legacy measurement. That profile is not corpus-canonical — the canonical statement is constant \(P_0 = 0.851\) since BBN. The Avrami-corrected framing has been reverted on this page; the canonical \(0.776\) prediction with a real \(\sim\!2\sigma\) tension stands. See Updates.

Python verification

The verification script for this observable is cosmology_tests.py. Run it with python3 cosmology_tests.py to reproduce the canonical \(S_8 ≈ 0.831 (, )\)–\(0.776\) result. The KiDS-Legacy measurement source: Wright et al. 2025.

References

• Wright et al. 2025 (KiDS-Legacy)
• Source paper: DCT-COS-01

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