Unified Internal Vector Gravity: Origin of the Dark Sector via Geometric Spontaneous Symmetry Breaking

AbstractThe standard cosmological model (ΛCDM) relies on two unexplained components—Dark Matter and Dark Energy—to reconcile galactic dynamics with cosmic expansion. We propose a fundamental revision of the gravitational composition law based on an ontological distinction between baryonic sources and the vacuum response field. In the Internal Vector Gravity (IVG) framework, the total gravitational field is not a scalar sum but the norm of a vector superposition in an internal 2D field space,𝑔tot =∥ 𝑔⃗𝑏 + 𝑔⃗𝑑 ∥𝜅.A Bayesian MCMC analysis of the SPARC database (3,252 rotation–curve data points) shows that galactic dynamics are governed by a specific destructive–interference state with coupling 𝜅gal = −0.712 ± 0.004,decisively rejecting both the orthogonal (κ=0) and scalar (κ=1) hypotheses withΔBIC > 104. We further show that cosmic acceleration emerges from a symmetry inversion of this coupling at low accelerations, saturating at 𝜅cosmo ≃ +0.75,so that “Dark Matter’’ and “Dark Energy’’ appear as two metastable phases of a single geometric interaction.This phenomenology is derived from a scalar–tensor Lagrangian with a spontaneous–symmetry–breaking potential, where baryonic matter tilts the vacuum potential and drives a dynamical transition from the constructive (accelerating) vacuum phase to the destructive (confining) matter phase. A Chameleon-like screening mechanism naturally restores Newtonian dynamics in high-density environments (𝜌 ≫ 𝜌gal ), with 𝑔tot → 𝑔Newton at Solar-System scales. The IVG framework thus resolves the Cosmic Coincidence Problem and predicts a present-day age of the Universe 𝑡0 ≈ 16 Gyr, alleviating the tension associated with the formation of massive high-redshift galaxies observed by JWST.