The Q-Rubin Framework, Version 3.3: Numerical Implementation and Forward-Model Tests

Abstract

We present Version 3.3 of the Q-Rubin framework, a covariant phenomenological ansatz for late-time energy exchange between a pressureless matter-like sector and an emergent dark sector on a four-dimensional brane. Version 3.3 retains the theoretical structure of Version 3.2 and adds the results of a numerical implementation in the Cosmic Linear Anisotropy Solving System (CLASS v3.3.4). The interaction is represented by a transfer current J^mu = M_Q^4 A(a) grad^mu phi_Q + M_Q^5 B(a) phi_Q u^mu decomposed into an energy-transfer scalar and orthogonal momentum-transfer vector. Early-time shielding is implemented through a bounded activation window and a hyperbolic relaxation-diffusion sector. The modified CLASS implementation was subjected to a zero-coupling control, parameter-recognition checks, clean-build reproduction, and active-coupling experiments. The uncoupled control calculation reproduces the reference CLASS Lambda-CDM baseline, S_8 = sigma_8 sqrt(Omega_m / 0.3) = 0.8378, for the cosmological parameter set used in the experiment. In the active parameter sweep, the reported A_0 = B_0 = 10^-12 case yields S_8 = 0.8094, corresponding to a 3.39% decrease relative to the baseline. An exploratory A_0 = B_0 = 10^-11 case gives S_8 = 0.6309. These are numerical model outputs from controlled CLASS forward experiments at fixed representative cosmological parameters, not observationally fitted constraints. The V3.2 manuscript contained an ambiguity in notation by using H for both the conformal and cosmic-time Hubble rates. Version 3.3 corrects this by using Script-H = a'/a and H = a-dot/a = Script-H/a throughout the numerical discussion. The corresponding CLASS implementation was audited using this distinction and the comoving-density formulation. The Q-Rubin source is publicly versioned in the repository at https://github.com/Q-Rubin/class_qrubin_clean, with the implementation associated with the numerical results reported here pinned to commit https://github.com/Q-Rubin/class_qrubin_clean/commit/a36716f1, which serves as the reproducibility anchor for the calculations presented in this work. The results demonstrate reproducibility of the implemented calculations for the tested configurations. They do not constitute observational evidence that Q-Rubin is preferred by cosmological data. A subsequent likelihood analysis against CMB, BAO, supernova, lensing, clustering, and growth data is required before any claim of tension resolution can be made.