sigma-8 tension

The sigma-8 tension (aka S8 tension or similar) is a contradiction between Lambda-CDM model parameter-determinations based on different kinds of observation data. Among the different kinds of data producing conflicts is that of the cosmic microwave background (CMB) versus that of observed nearby galaxy clusters (i.e., galaxy clusters in their recent state, e.g., with z < 1). Calculated Lambda-CDM parameter sigma-8 (aka σ₈ or similar) values from the two kinds of observations show the conflicting values, as do values of the derived parameter, S₈ (aka S8 or similar):

S8 = σ8 × (Ωm/0.3)1/2

• Ω_m - matter density parameter.
• σ₈ - a quantification of matter density fluctuations on a scale (8 h^-1 Mpc), which is intended for comparison with galaxy-cluster observation data.

Note that Ω_m determinations are generally close to 0.3, making (Ω_m/0.3)^1/2 close to 1, giving S8 and σ₈ similar numerical values; thus it is easy to mistake the value of one for that of the other. (I believe S8 was devised as an "adjusted Sigma-8", that takes into account one factor that would make Sigma-8 differ from recent galaxy-cluster-based determinations.) To demonstrate the discrepancy, one recent CMB-based S8 determination placed it very likely within two hundredths of 0.834, whereas recent determinations based on observation of galaxy clusters are lower, one such determination placing it very likely within two hundredths of 0.769. Any value likely according to one of the types of determination is very unlikely according to determinations of the other type. Like the Hubble tension, the S8 tension is one of the anomalies of major current interest regarding the Lambda CDM model and current observation. The discrepancy has motivated attempts to invent better analysis, proposals of additional factors that could explain the difference, and the checking of alternative cosmologies to see if any do not show the discrepancy.