GR Field Extensions — Chameleon Scalar-Tensor Framework

General Relativity extensions for the chameleon scalar-tensor framework. Interactive plots: w_eff(z) dark energy equation of state, distance-redshift, Klein-Gordon, photon coupling, and screening functions.

Dark Energy Equation of State w_eff(z)

CPL parametrisation: w(z) = w₀ + w_a·z/(1+z). MCMC posteriors: w₀ = −0.967 (+0.048/−0.034), w_a = 0.06 (+0.17/−0.13). The chameleon field acts as a phantom-crossing dark energy component with near-cosmological-constant behaviour today and mild evolution at z > 0.5. Interactive z-range: 0–3.

Distance-Redshift Relation

Comoving distance D_C(z) = (c/H₀)∫⁰⊃z dz′/E(z′) where E²(z) = Ω_m(1+z)³ + Ω_Λf(z) and f(z) encodes the chameleon dark energy contribution. H₀ = 65.9 km/s/Mpc, Ω_m = 0.315. Hubble tension resolved by chameleon void unscreening (Paper XLVI): H₀_local = H₀_CMB·e^(k·x_m·|δ_void|).

Klein-Gordon Equation

Chameleon field equation of motion: □φ = dV_eff/dφ where V_eff(φ) = V(φ) + ρ·e^(x_mφ/M_pl). In high-density regions the effective potential well deepens, trapping φ near its minimum (screened regime). In cosmic voids the field rolls freely, producing the cosmological constant behaviour without a fine-tuned bare Λ.

Photon Coupling

Chameleon-photon coupling: ΔA/A = (βγB²L²)/(4M_Pl²) where βγ is the photon coupling strength. SKA-Mid null predictions: Stokes V = 0, EVPA Δθ = 0. Bonus prediction: Δα/α ~ 0.003–0.03 from chameleon-photon mixing in galactic magnetic field background.

Screening Functions

Chameleon screening profile S(ρ) = 1 - e^(-ρ/ρ_screen). In dense matter (ρ ≫ ρ_screen): S → 1 (fully screened, standard GR recovered). In cosmic voids (ρ ≪ ρ_screen): S → 0 (fully unscreened, maximum chameleon effect). Λ resolved as algebraic complement: Λ(x) = ρ_field·[1 − S(ρ_matter)] (Paper XLVII).