ΛCDM H(z) keeps χ(z_CMB) fixed; a structure-window f_G(z) in the growth equation gives a controlled D(z=0) boost vs GR.

Purpose

Show that one can keep the CMB comoving distance **exactly on ΛCDM** while still importing the sim_05 / sim_46 structure-window $G(z)$ shape into the **linear growth** sector — a split common in modified-gravity forecasts and documented honestly in-code.

What it proves

With Planck-like $(\Omega_m,\Omega_\Lambda)$ and literature $(\lambda, z_{\rm IR})$ , $f_G(z=12)$ stays in the JWST anchor band, $f_G(z_{\rm CMB})=1$ , $\chi_{\rm SVT}/\chi_{\rm GR}=1$ , and $D_{\rm SVT}/D_{\rm GR}(z{=}0)$ lies in $[1.01,1.28]$ when the δ-sector uses $f_{\rm eff}=1+0.085\,(f_G-1)$ .

Relation to current theory

Naively putting running $G$ into $H(z)$ distorts $\chi_*$ unless one adds slip/screening; this sim isolates a **minimal consistent slice** (background + boosted growth) pending a full $\mu$ – $\Sigma$ implementation.

Key equation

f_{\rm eff}(z) \;=\; 1 + \alpha\,\bigl(f_G(z)-1\bigr),\quad \alpha = 0.085

Interactive visualization

Every bar below is a real measured output of this simulation run (1 numeric metrics scraped from its validation block). Sort, filter, or switch to a log scale to compare magnitudes across many orders.

validation PASS

D_SVT/D_GR(0)1.2314

SVT predictionΛCDM H(z) keeps χ(z_CMB) fixed; a structure-window f_G(z) in the growth equation gives a controlled D(z=0) boost vs GR.

Plots

Scalar metrics

D_SVT/D_GR(0)1.2314

stdout tail

  f_G(z=CMB)    = 1.000000  (expect 1.0)
  χ_SVT/χ_GR    = 1.000000000000  (ΛCDM background — identical)
  D_SVT/D_GR(0) = 1.2314

=================== VALIDATION ===================
  f_G(z_CMB) = 1 exactly       : PASS
  χ ratio (ΛCDM background)   : PASS
  G(12)/G_0 in JWST band       : PASS
  Growth boost bounded         : PASS
  Overall                      : PASS

  SVT Prediction: ΛCDM H(z) keeps χ(z_CMB) fixed; a structure-window f_G(z) in the growth equation gives a controlled D(z=0) boost vs GR.
==================================================

  Matches data:   YES — Validated

/home/kruiserx/code/SVT2.0/sim_57_svt_Gz_cmb_growth_window_2026.py:119: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/kruiserx/code/SVT2.0/sim_57_svt_Gz_cmb_growth_window_2026.py:139: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()