Microphysical Yield Model for Cosmic Expansion: Environmental Hubble Rates and a Notebook-Based Audit with Cosmic Chronometers and Radial BAO

This work proposes an operational, microphysics-motivated parameterization of the cosmic expansion rate in which the present-day Hubble scale is interpreted as a very small dimensionless yield per microscopic cycle. The central idea is that a baseline expansion rate can be written in terms of a fundamental “clock” frequency associated with the electron and a dimensionless coupling ratio comparing gravitational to electromagnetic interaction strengths for a proton–electron pair. Core definitions and model structure Observed yield (dimensionless):Y_obs is defined as H0 / (2π ω_e), i.e., the fraction of “expansion per cycle” of a microscopic frequency scale. Microphysical yield hypothesis:The yield is identified (up to order-unity factors) with the dimensionless ratioq_GE = (G m_p m_e) / (k_e e^2),comparing gravitational attraction to electromagnetic coupling for the proton–electron system. Baseline microphysical expansion rate:H_micro = 2π q_GE ω_e.Numerically this evaluates to a Hubble-scale rate of order ~66 km/s/Mpc, close to early-universe inferences (e.g., CMB-based determinations), without introducing free cosmological parameters for H0. To connect this baseline with late-time measurements, the model introduces: A quasi-free expansion scale H_vac defined from the empirical low-acceleration scale a0 via H_vac = 2π a0 / c (order ~78 km/s/Mpc). An excess ΔH = H_vac − H_micro. A vacuum-fraction function f_vac(z), operationally approximated by the standard vacuum energy fraction F_Λ(z) when detailed void/filament volume data are unavailable. A high-redshift closure term to recover the correct matter- and radiation-dominated scalings at large redshift, implemented through a Friedmann-like quadratic sum that reproduces H(z) ∝ (1+z)^(3/2) (matter) and H(z) ∝ (1+z)^2 (radiation). Environmental interpretation (what varies and why) In this framework, the baseline H_micro is treated as universal, while observed H(z) depends on how expansion “propagates” through structured environments. To capture this, the model includes: An intrinsic inertial locking parameter η_intr that reduces the effective expansion rate in dense regions. A linear structure growth factor D(z), implemented in two ways: a common semi-analytic approximation (literature-based), and a numerically integrated self-consistent solution. Three effective regimes: “void-like” (minimal locking), “wall-like” (maximal locking), “volume-averaged” (intermediate, weighted by f_vac). This produces a concrete mechanism for why different probes can return different effective H0 values: they sample different mixtures of void-dominated and wall-dominated regions across their lines of sight and redshift ranges. Data confrontation and reproducibility The accompanying notebook performs a point-by-point audit against: Cosmic Chronometers (CC): direct H(z) estimates from passive galaxy age gradients. Radial BAO: measurements of D_H(z)/r_d, with r_d treated as a nuisance scale fitted only to the BAO data in this audit. For each data point, the notebook reports: the model prediction, the residual and normalized pull, PASS/FAIL based on a 2-sigma rule, global chi-square summaries. All tables and figures shown in the manuscript are exported directly by the notebook (CSV for point-by-point tables and PNG for plots). The intent is that readers can reproduce the reported numbers by running the notebook and comparing the generated artifacts. Scope, limitations, and how to read the results This is an explicitly phenomenological/operational proposal designed to be testable and falsifiable with standard expansion observables, not a complete alternative to ΛCDM. Key limitations in the current version include: f_vac(z) is approximated by a density-fraction proxy rather than derived from explicit void/filament volume catalogs at each redshift. The high-redshift closure is introduced to recover known scaling laws, rather than derived from first principles within a fully covariant theory. Only CC and radial BAO are used in the main quantitative audit; transverse BAO, supernova distances, strong-lens time delays, and the full CMB spectrum are discussed as future work. Included files Manuscript PDF. Jupyter notebook (the analysis pipeline). Exported CSV tables (point-by-point CC and BAO, summary parameters). Exported figures (residual plots and H(z) comparisons).