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06_RSD_fs8: structure-growth-rate window
V30-30.6 · F 证据节 / 显影节 ·
30.6 extends V30’s early_growth_window from the toy CMB leg into late-time structure growth: using 15 fσ8(z) measurements, one shared Gaussian χ² likelihood, flat ΛCDM background geometry on both sides, and a 2D-versus-3D grid-search comparison in which the Energy Filament Theory (EFT) side frees γ, the report lands at ΔBIC = +1.932 and ΔAICc = +2.406, so the section is kept as a weak-equivalence growth ledger rather than a uniqueness verdict, with the no-MCMC boundary left explicit.
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Keywords: Energy Filament Theory, EFT, RSD, fσ8, growth-rate ledger, gamma extension, grid search, early_growth_window, weak equivalence, BAO bridge, ISW×LSS interface, cluster extension
Section knowledge units
thesis
30.6 is the growth-rate leg of Volume 30’s early_growth_window. Using 15 fσ8(z) measurements, the report compares flat ΛCDM with an EFT-gamma extension under the same data and likelihood scaffold. Because the score table leaves ΔBIC = +1.932 (EFT − ΛCDM) inside the report’s equivalence zone while ΔAICc = +2.406 only mildly favors ΛCDM, the section is kept as a weak-equivalence growth ledger rather than as a uniqueness verdict. In V30 it therefore weakens exclusivity at the structure-growth layer without claiming that RSD prefers EFT.
mechanism
The comparison frame is intentionally spare and auditable. The data source is rsd_fs8_clean.csv with 15 points, and both sides use the same Gaussian chi-square χ² = Σ (obs-model)²/σ² with unit weights. Flat ΛCDM varies {Ω_m0, σ8_0} while keeping γ = 0.545 fixed; the EFT-gamma side varies {Ω_m0, σ8_0, γ}. Just as important, the background geometry is flat ΛCDM for both models. That means 30.6 is not a full alternative-background cosmology test; it is a controlled γ-extension window for late-time growth.
evidence
The numerical table is mixed but not decisive. Flat ΛCDM returns Ω_m0 = 0.315, σ8_0 = 0.77, χ² = 4.146, AICc = 9.146, and BIC = 9.562. EFT-gamma returns Ω_m0 = 0.10, σ8_0 = 0.84, γ = 0.30, χ² = 3.370, AICc = 11.552, and BIC = 11.494. EFT therefore reaches the lower χ² but pays a complexity penalty. The report’s own reading is that ΔBIC = +1.932 still belongs to weak equivalence, while ΔAICc = +2.406 is only a mild, non-significant lean toward flat ΛCDM. So the observable does not uniquely select ΛCDM.
boundary
The boundary is explicit rather than hidden. Flat ΛCDM is fit by a 2D grid search and EFT-gamma by a 3D grid search; no MCMC layer is used, and AICc/BIC are the primary diagnostic outputs. The source also states that AICc mildly prefers ΛCDM, even though the overall conclusion remains weak equivalence. Combined with the shared flat-ΛCDM background geometry, that means 30.6 should not be inflated into a full growth-of-structure or background-expansion verdict. Its narrower claim is that, in this 15-point RSD ledger, growth-rate data do not uniquely select ΛCDM.
interface
The reproducibility block is compact and sufficient: rsd_fs8_clean.csv, rsd_lcdm_baseline_results.json, rsd_eft_gamma_results.json, plus the PowerShell run scripts for the flat ΛCDM baseline and the EFT gamma run. Inside Volume 30, 30.6 sits between 30.5’s toy CMB phase-damping window and 30.10’s ISW×LSS late-potential return, while also bridging laterally toward 30.7’s BAO geometry interface and outward toward 30.9’s cluster-scale extension. Its job is to connect geometry and growth under one report-bundle grammar, not to author EFT ontology.