Cosmic Structure Without Standard Candles: Robust Inference of Growth and Expansion in the ΛUTCU Model

📝 Work Summary (Description) This repository contains the second critical validation phase of the $\Lambda$UTCU (Universal Cosmic Transfer Unit) model. While the previous analysis was a joint effort, this study isolates the Large Scale Structure (LSS) sector to validate the TCU V9 metric independently of luminosity distance indicators (Supernovae Ia). ✅ What does this work do? Independent Geometric Validation: Demonstrates that the TCU V9 metric fits the expansion history using exclusively Baryon Acoustic Oscillations (BAO) and Redshift Space Distortions (RSD). Precision in Growth Dynamics: Solves the full growth differential equations, achieving a highly consistent fit ($\chi^2_{red} \approx 0.78$) with eBOSS DR16 data, without the $\Lambda$CDM "standard" bias. H-Infinity Stability: Extracts an asymptotic Hubble parameter of $H_{\infty} \approx 64.21$ km/s/Mpc, aligning with early-universe estimates. 🛠️ Technical Note for the Reviewer (Analysis & Visualizations) To ensure scientific reproducibility and clinical robustness, this repository provides: General Metric Analysis: Full implementation of the TCU V9 modified Friedmann equations. MCMC Inference Engine: Detailed Monte Carlo Markov Chain traces and corner plots showing parameter convergence. Fit and Dispersion Plots: High-resolution visualizations comparing the theoretical predictions of $f\sigma_8(z)$, $D_M(z)$, and $D_H(z)$ against the SDSS/eBOSS data points. Residual Analysis: Statistical diagnostic plots showing the residuals of the fit, confirming the absence of systematic offsets and proving the metric's accuracy. 📊 File Contents [Your_New_Filename].ipynb: Python source code featuring the complete pipeline, from eBOSS covariance matrix loading to MCMC execution. Diagnostic Visualizations: MCMC corner plots and comparative structure growth charts. ⚖️ License and Citation This work is distributed under the Creative Commons Attribution 4.0 International license. Please cite this analysis as the "Geometric Sector Validation" of the TCU V9 project.