CCEGA: A Unified 5D Geometric Framework

CCEGA: A Unified Geometric Framework with Falsifiable Predictions at the Electroweak Scale

Author: López Sánchez, Marc

Abstract:

We present the CCEGA (Curvature Brake Enhanced General Approximation) framework, an effective five-dimensional theory that simultaneously addresses the mass hierarchy problem and the existence of gravitational singularities through a dynamical "Curvature Brake" mechanism. Unlike previous extra-dimensional scenarios, CCEGA is strictly falsifiable, establishing a direct and verifiable link between 5D geometric stability and immediate empirical observables.

The framework predicts that the hierarchical amplification factor (\Xi \sim 10^{34}) anchors both the cosmological bounce and the black hole regularization scale at approximately 100 GeV. This alignment with the electroweak scale yields three critical, falsifiable experimental signatures:

1. Gravitational Wave Signatures: We predict post-merger echoes with a characteristic time delay of \Delta t \approx 2GM \ln \Xi (where \ln \Xi \approx 78), accompanied by a "Spectral Comb" of sidebands induced by radion oscillations, detectable by LISA and the Einstein Telescope.
2. Collider Phenomenology: The model predicts a 3-12% suppression in Higgs Vector Boson Scattering (VBS) cross-sections at 100 TeV, providing a definitive target for the Future Circular Collider (FCC).
3. Cosmological Consistency: The Big Bounce occurs at a temperature (T_c \sim 100 GeV) compatible with Big Bang Nucleosynthesis (BBN), allowing for validation via tensor-to-scalar ratio modifications and B-mode polarization analysis in the Cosmic Microwave Background.

By providing these specific spectral and energetic targets, the CCEGA framework serves as a verifiable bridge between quantum gravity and experimental particle physics, defining a clear pathway to confirm or discard the physical reality of warped extra dimensions.

CCEGA (Freno de Curvatura a Partir de Dimensiones Extra Compactadas y Enfoque Geométrico), un marco unificado que aborda simultáneamente el problema de la jerarquía electrodébil de Planck y la evitación de singularidades cosmológicas y de agujeros negros. El modelo emplea una geometría deformada pentadimensional estabilizada donde la retrorreacción del radión modifica dinámicamente la tensión efectiva de la brana. A altas densidades de energía, este mecanismo invierte el signo del término de densidad cuadrática en la ecuación de Friedmann modificada, produciendo un rebote no singular. En el colapso gravitacional, el freno de curvatura reemplaza las singularidades con núcleos de densidad finita, generando ecos de ondas gravitacionales con retardos temporales. 

By integrating these references, it is highlighted that the proposal by López Sánchez, Marc, does not simply represent a logical extension of Randall-Sundrum scenarios, but provides a unified solution to questions that contemporary models only address in a partial or fragmented manner. The 'Curvature Brake' mechanism acts as the indispensable theoretical bridge connecting particle physics at the FCC scale with the next-generation gravitational wave astronomy represented by LISA.