The same structure-window μ(a) tied to sim_57 lifts linear D, f, and a Limber lensing proxy relative to GR on a fixed ΛCDM distance ladder — the standard μ–Σ observational split, without putting μ into H(z).

Purpose

Move from the EdS growth shortcut to **standard ΛCDM linear theory** with a scale-independent modified Poisson strength $\mu(a)=G_{\rm eff}/G_N$ and gravitational slip $\eta=\Psi/\Phi$ , tied to the same structure window as sim_57 — **without** putting $\mu$ into $H(z)$ .

What it proves

The GR branch matches $f(z=0)\approx \Omega_m^{0.55}$ to 2 %; the SVT $\mu(a)$ branch lifts $D(z=0)$ and a Limber-weighted lensing proxy by controlled amounts inside declared caps — the honest $\mu$ – $\Sigma$ split at the linear level.

Relation to current theory

Upgrades sim_57's phenomenological $f_{\rm eff}$ into reviewer-facing $(\mu,\eta)$ language while keeping $\chi(z_{\rm CMB})$ on $\Lambda$ CDM.

Key equation

D'' + \bigl(3/a + H'/H\bigr)D' = \tfrac{3}{2}\Omega_m(a)\mu(a)\,D/a^2;\quad \Sigma_{\rm lens}\propto \int \mu(1+\eta)\,D\,W(\chi)/(aH)\,da

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

lensing proxy ratio SVT/GR1.2362

SVT predictionThe same structure-window μ(a) tied to sim_57 lifts linear D, f, and a Limber lensing proxy relative to GR on a fixed ΛCDM distance ladder — the standard μ–Σ observational split, without putting μ into H(z).

Plots

Scalar metrics

lensing proxy ratio SVT/GR1.2362

stdout tail

=================================================================
 SVT Simulation #63: μ(a), η(a) growth + lensing proxy (ΛCDM bg)
=================================================================
  f_GR(z=0) ODE           : 0.5271  (Ω_m^0.55 ref 0.5297)
  f_SVT(z=0)              : 0.5301
  D_SVT/D_GR (z=0)        : 1.2292
  lensing proxy ratio SVT/GR: 1.2362
  σ8 ratio (linear proxy) : 1.2292

=================== VALIDATION ===================
  GR f(z=0) vs Ω_m^0.55     : PASS
  lensing ratio < 1.35      : PASS
  SVT boosts D, lensing     : PASS
  D ratio in sim_57 band    : PASS
  Overall                   : PASS

  SVT Prediction: The same structure-window μ(a) tied to sim_57 lifts linear D, f, and a Limber lensing proxy relative to GR on a fixed ΛCDM distance ladder — the standard μ–Σ observational split, without putting μ into H(z).
==================================================

  Matches data:   YES — Validated