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Scale-dependent Hubble
S.T.A.R. treats the local expansion rate as a weighted real-period average plus entropy-curvature and metric-trace terms that decay toward last scatter. This is a phenomenological layer on ACSC, not a derivation from the RTCH action.
Heff(z) = HΛCDM(z; H₀ ⟨Ω⟩_z) + β κ(z) + γ Tr(δg)
H0_eff(z)
72.62km/s/Mpc
z = 0.00
SH0ES
73.04km/s/Mpc
local ladder
Planck
67.4km/s/Mpc
CMB
H_eff(z*)
67.40
last scatter
Inferred H0 versus redshift
Controls
redshift z0.00
entropy curvature β0.48
metric trace γ0.22
⟨Ω_E⟩_z
0.9958
κ_UCF = 31.5926
Cluster probe
Illustrative nearby overdensities used as a local sampling check, not a survey catalog.
Virgo
54 Mly · rank 2
1.0174
Perseus
236 Mly · rank 1
1.0237
Coma
321 Mly · rank 0
1.0251
Hercules
500 Mly · rank 1
1.0270
Shapley
650 Mly · rank 1
1.0281