A Quadratic Volume-Dependent Space Tension Constant Solution to the Hubble Tension and the Big Rip Paradox: The Çelik Model

The standard cosmological model (ΛCDM) attributes the accelerated expansion of the universe to a constant dark energy density (ρΛ). However, this model faces the critical Hubble Tension, a persistent discrepancy between Early Universe measurements (67.4 km/s/Mpc via CMB) and Late Universe local observations (73.0 km/s/Mpc via Supernovae). Furthermore, a constant equation of state parameter (w = −1) leads to the Big Rip paradox. In this paper, we propose that the Hubble discrepancy is not a calibration error but the exact missing mass-energy signature of a universal restoring force. We introduce the Çelik Space Tension Constant (S), an innate cosmological braking mechanism that scales with the square of the observable universe's volume (V²). By deriving S ≈ 4.2 × 10⁻¹⁰⁸ kg/m⁶, we formulate a dynamic cosmic energy equation. This quadratic tension implies that dark energy will eventually be neutralized, defining a theoretical Maximum Volume Limit (Vmax) and preventing the Big Rip. Recent data from the Dark Energy Spectroscopic Instrument (DESI) suggesting a dynamical, weakening dark energy strongly supports the phenomenological predictions of the Çelik Model. Version 2 Update: This comprehensive version includes Appendices A through F, detailing the tensor dynamics, quantum origin, and gauge-invariant formulation of the Çelik Model. Furthermore, it introduces robust statistical validation via Markov Chain Monte Carlo (MCMC) simulations against the Cosmic Chronometers and Pantheon+ Supernovae datasets. The open-source Python simulation codes and the resulting parameter space contour plots are provided as supplementary materials in this record.