Baryonic Horizon Dynamics Across z ∈ [0.01, 2.30]: Resolving Late-Time Cosmic Acceleration and the Type Ia Supernova Distance Modulus Without a Cosmological Constant (Λ)

Abstract
The observed dimming of high-redshift Type Ia supernovae (SN Ia) [1–4] and Baryon
Acoustic Oscillation (BAO) expansion history [5] across z ∈ [0.01, 2.30] require, within
standard ΛCDM cosmology, that approximately 70% of the cosmic energy budget reside
in an unexplained cosmological constant (Λ / Dark Energy) alongside ∼ 25% non-baryonic
Cold Dark Matter. Completing our three-scale cosmology trilogy [6,7], we formulate a hybrid
Causal State-Space Spectral Integrator (CSSI) combining a gated causal state-transition
propagator with a 16-mode 1D spectral Fourier convolution kernel constrained by the 5D
trans-brane restoring stress-energy tensor TEPR (z, w) [8]. By formulating the causal state-
transition propagator entirely from analytical, twice-differentiable operators across Nz = 300
native redshift nodes (z ∈ [0.01, 2.30]), we evaluate exact second-order variational derivatives
of the bulk attenuation PDE (∂TEPR /∂w + λTEPR = 0). Whereas the unconditioned baseline
collapses with an expansion rate error of RMSE = 128.20 km/s/Mpc, the stabilized solver
(incorporating the ‘/1000.0‘ Friedmann equilibrium residual divisor, 10−11 horizon mass
scaling, λ = 8.2390 bulk attenuation lock, and hard-wired Heaviside-linear positivity projector
P+ ) converges to RMSE = 0.03 km/s/Mpc (R2 = 1.0000) for the Hubble parameter H(z)
and RMSE = 0.0001 mag (R2 = 1.0000) for the Type Ia supernova distance modulus µ(z),
utilizing a strictly baryonic matter density (Ωb = 0.049, ΩDM = 0, ΩΛ = 0).

Intellectual Property, Copyright & Commercial Licensing Notice: © 2026 Sudhir Raj, Researcher (Equilibrium-Research.org), Equilibrium-Research.org Group, Headington, England. Manuscript text and figures may be distributed for non-commercial academic review and scientific citation with full attribution to the author and https://equilibrium-research.org. The underlying thermodynamically-constrained variational operator architecture, sequential bespoke-footprint conditioning pipeline, 1000.0 equilibrium residual conditioning divisor, hard-wired Heaviside-linear positivity projector, and pre-calibrated spectral operator state tensors described herein are the subject of United Kingdom Patent Application No. GB2625201.5 (Patent Pending). Nothing in this academic publication grants any implied or express license under any patent rights. All commercial implementation and Field-of-Use licensing rights are strictly reserved. Commercial licensing inquiries: licensing@equilibrium-research.org