What does this equation mean?

The second, quieter disagreement is the S8 tension. S8 is a combination of the amplitude of matter density fluctuations $\sigma_8$ and the matter density parameter $\Omega_m$ , defined as $S_8 \equiv \sigma_8 \sqrt{\Omega_m / 0.3}$. 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 release remains on the low side [ 7 ] . That instability is itself informative: it is closer to what a systematic-error story predicts than what a new-physics story predicts, a point the comparison below returns to.