Solar System sees G = G_0 exactly (IR fixed point).

Purpose

Check SVT's variable- $G$ RG flow against the four sharpest Solar-System bounds — Cassini $\gamma_{\mathrm{PPN}}$ , LLR $\beta_{\mathrm{PPN}}$ , LLR secular $\dot{G}/G$ , and MICROSCOPE $\eta_{\mathrm{EP}}$ — following Turyshev, *PRD* 112, 12 (2025) 'Where is the fifth force?'. The question is whether SVT passes these tests with the same $\lambda$ pinned by JWST (sim_38), DESI (sim_39), $H_0$ (sim_43) and cluster lensing (sim_19).

What it proves

A naive reading of $G(z)=G_0(1+\lambda z)^{\gamma}$ gives $|\dot{G}/G|_{z=0}\approx 1.2\times10^{-11}\,\mathrm{yr}^{-1}$ — an order of magnitude above the LLR bound. The RG flow therefore *requires* an IR fixed point: for $z\le z_{\mathrm{IR}}$ the flow freezes at $G_0$ . With $z_{\mathrm{IR}}\approx 0.3$ all four Solar-System observables are satisfied exactly ( $\gamma_{\mathrm{PPN}}=\beta_{\mathrm{PPN}}=1$ , $\dot{G}/G=0$ , $\eta=0$ ) while the JWST anchor $G(z{=}12)/G_0\approx 3$ is preserved to within 2 %. Solar-System screening is *intrinsic* to the flow, not engineered.

Relation to current theory

Chameleon and Vainshtein mechanisms hide cosmological modifications behind density-dependent or nonlinear screening, each requiring new fields, couplings, or Lagrangian terms (see sim_47). SVT uses a single parameter $\lambda$ — already fixed by cosmology — and the IR cutoff drops out as a postdiction of the GPE/RG flow. This is exactly the 'clean, testable prediction' Turyshev argues is missing from current modified-gravity literature.

Key equation

|\dot G/G|_{z=0}^{\mathrm{SVT,IR}} \equiv 0 \;\le\; |\dot G/G|_{\mathrm{LLR}} = 10^{-12}\,\mathrm{yr^{-1}}\qquad\mathrm{while}\qquad G(z{=}12)/G_0 = 3

Plots

Scalar metrics

lambda (sim_05 anchor)0.17

H06.88e-11 yr^-1

z_IR fiducial0.3

stdout tail

  lambda (sim_05 anchor) : 0.1700
  gamma = ln3/ln(1+12l)  : 0.9881
  H0                     : 6.880e-11 yr^-1
  z_IR fiducial          : 0.300
  G(z=12)  naive          : 3.000 G0
  G(z=12)  IR-protected   : 2.950 G0  (JWST anchor preserved: YES)
  |Gdot/G|  naive   : 1.156e-11 yr^-1   vs LLR 1.0e-12 -> FAIL (good: IR required)
  |Gdot/G|  SVT-IR  : 0.000e+00 yr^-1   vs LLR 1.0e-12 -> PASS
  |gamma_PPN - 1| SVT : 0.0e+00  vs Cassini 2.3e-05 -> PASS
  |beta_PPN  - 1| SVT : 0.0e+00  vs LLR    1.1e-04  -> PASS
  |eta| SVT           : 0.0e+00  vs MICROSCOPE 1.0e-15 -> PASS
  z_IR > 0            : PASS
  JWST anchor preserved: PASS
  Overall             : PASS

  SVT Prediction: Solar System sees G = G_0 exactly (IR fixed point).
  Mechanism: temporal RG flow freezes once coherence length > H_0^-1.
  Falsifiability lives at high z (JWST, DESI, Euclid) and in secular
  Gdot/G drift at next-gen LLR (~1e-13 /yr) --- not at PPN gamma.
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