Sigma_8 Evolution Kink

Beyond the static S₈ tension, observations of the growth of structure over cosmic time reveal a subtler anomaly: the rate at which clustering grows appears to slow down or 'kink' at redshifts z ~ 0.5–1 in a way that ΛCDM does not predict. Redshift-space distortion measurements from galaxy surveys (BOSS, eBOSS, VIPERS) parameterize growth through f σ₈, where f is the linear growth rate and σ₈ is the amplitude of fluctuations. Compiled across multiple surveys, the data shows a systematic downward trend relative to the Planck ΛCDM prediction — not just a uniform offset but a shape difference that suggests the growth history itself is wrong.

ΛCDM's growth function is determined entirely by the matter density and dark energy equation of state — both fixed in the standard model. A kink or suppression in growth at intermediate redshifts could signal modified gravity (GR breaking down on large scales), early dark energy that subsequently decayed, or additional species (interacting dark matter, sterile neutrinos) that suppressed growth at specific epochs. None of these solutions can be incorporated into ΛCDM without abandoning core assumptions. The σ₈ evolution anomaly is distinct from the static S₈ tension and, if confirmed at higher significance, would require a qualitatively different explanation.