LoE Cosmology v4.0 A Relational Effective Theory of Cosmic Expansion with Predictive JRΦ Dynamics

LoE Cosmology v4.0 — A Predictive Relational Effective Theory of Cosmic Expansion

Description:
LoE Cosmology v4.0 introduces the first complete simulation-ready formulation of Logic of Existence (LoE) as an alternative cosmological framework.
In LoE, spacetime, curvature, and energy density emerge from the dynamics of three relational intensities:

(J,R,Φ),(J, R, \Phi),(J,R,Φ),

frozen during inflation and governing cosmic evolution at all later epochs.

A cosmological patch is represented as an LoE-triangle, whose geometric area—scaled by the inflation-born constant ccc—produces an effective energy density:

ρLoE(z)=λcosmo c Ageom(R1,R2,R3).\rho_{\mathrm{LoE}}(z) = \lambda_{\mathrm{cosmo}}\, c\, A_{\mathrm{geom}}(R_1,R_2,R_3).ρLoE(z)=λcosmocAgeom(R1,R2,R3).

Inserted into a generalized LoE–Friedmann equation,

H2(z)=8πG3ρLoE(z),H^2(z)=\frac{8\pi G}{3}\rho_{\mathrm{LoE}}(z),H2(z)=38πGρLoE(z),

this density yields explicit and testable predictions for the expansion history of the Universe.

Version 4.0 includes:

🔹 Full JRΦ dynamical system

A Hamiltonian-driven evolution of relational fields:

R˙, J˙, Φ˙\dot R,\ \dot J,\ \dot\PhiR˙, J˙, Φ˙

which governs geometry, energy and cosmic expansion.

🔹 Explicit redshift-dependent relational models R(z)

Including:

• frozen relic fields,

• power-law drift,

• oscillatory corrections.

Each generates distinct observational signatures.

🔹 First LoE simulation plots

Including:

• evolution of R(z)R(z)R(z),

• predicted expansion rate H(z)H(z)H(z).

These show how small relational drifts produce the observed acceleration.

🔹 Relational explanation of dark energy

Dark energy is not vacuum energy but an effective emergent quantity:

Λeff(z)=8πG3ρLoE(z).\Lambda_{\mathrm{eff}}(z) = \frac{8\pi G}{3}\rho_{\mathrm{LoE}}(z).Λeff(z)=38πGρLoE(z).

🔹 Natural resolution of the Hubble tension

Local and global Hubble measurements probe different relational coarse-grainings:

Hlocal≠HCMB.H_{\mathrm{local}} \neq H_{\mathrm{CMB}}.Hlocal=HCMB.

LoE predicts this divergence without modifying GR.

🔹 Relational perturbations and primordial structure

Density perturbations arise from:

δ(J,R,Φ)⇒δρLoE,\delta(J,R,\Phi) \quad\Rightarrow\quad \delta \rho_{\mathrm{LoE}},δ(J,R,Φ)⇒δρLoE,

yielding a non-standard relational power spectrum.

🔹 Clear observational predictions

LoE Cosmology v4.0 predicts:

• scale-dependent deviations in H(z)H(z)H(z),

• small oscillatory signatures from R(z)R(z)R(z),

• modified BAO scale,

• non-standard primordial spectrum,

• redshift drift distinct from Λ\LambdaΛCDM.

Keywords:
LoE, Logic of Existence, cosmology, relational physics, effective theory, dark energy, Hubble tension, JRΦ dynamics, alternative to ΛCDM, emergent constants, inflation, expansion history, H(z), large-scale structure.

Version:
v4.0 — Simulation Edition