LoE Cosmology v3.0 A Relational Alternative to ΛCDM with Predictive Dynamics

LoE Cosmology v3.0 — A Relational Effective Theory of Cosmic Expansion

Description:
LoE Cosmology v3.0 presents a complete, predictive formulation of Logic of Existence (LoE) as an effective cosmological framework.
In LoE, space-time and energy are not fundamental objects but emergent consequences of relational intensities between nodes of existence:

(J,R,Φ).(J, R, \Phi).(J,R,Φ).

The model reconstructs cosmic geometry using LoE-triangles, where each cosmological patch is encoded by three relational strengths RijR_{ij}Rij. Their geometric area, scaled by the inflation-born constant ccc, yields 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).

This density directly enters 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),

making cosmic expansion a relational process rather than the result of an external vacuum energy.

Version 3.0 introduces:

• full dynamical equations for the relational fields J,R,ΦJ, R, \PhiJ,R,Φ,

• explicit redshift-dependent models Ri(z)R_i(z)Ri(z),

• example predictions for the expansion history H(z)H(z)H(z),

• a natural explanation of the Hubble tension via relational inhomogeneity,

• a relational mechanism for primordial perturbations,

• an emergent interpretation of the cosmological constant,

• testable deviations from Λ\LambdaΛCDM.

This work unifies dark energy, inflationary relics, and structure formation into a single relational framework, offering an alternative perspective on cosmology grounded in the Logic of Existence.

Keywords:
LoE, Logic of Existence, cosmology, effective theory, relational physics, dark energy, Hubble tension, inflation, H(z)H(z)H(z), emergent constants, JRΦ, alternative to ΛCDM, fundamental physics

Version:
v3.0 (Extended Framework)