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Equation 3 · Part 4 · Comparing the Main Approaches to Precision Cosmology

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S8≡σ8Ωm/0.3S_8 \equiv \sigma_8 \sqrt{\Omega_m / 0.3}
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The second, quieter disagreement is the S8 tension. S8 is a combination of the amplitude of matter density fluctuations σ8\sigma_8 and the matter density parameter Ωm\Omega_m , defined as S8≡σ8Ωm/0.3S_8 \equiv \sigma_8 \sqrt{\Omega_m / 0.3}. Weak gravitational lensing surveys — which measure the distortion of background galaxy shapes by intervening matter, and therefore probe how clustered matter actually is in the late universe — have historically reported S8 values a few percent below what Planck’s early-universe fit predicts [ 7 ] . This tension has been smaller and less consistent across surveys than the Hubble tension; the 2025 KiDS Legacy reanalysis, notably, shifted upward into consistency with Planck, while DES’s Y6…

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