A Dynamic Unified Metric: Cosmological Expansion, Black Hole Geometry, and Scalar Field Coupling from a Generalized Kottler Framework

Failure to find a unified geometrical description of the expansion of the Universe and black hole physics continues to be one of the central issues in theoretical physics today. This paper proposes a Dynamic Unified Metric, constructed by generalizing the Kottler (Schwarzschild-de-Sitter) solution with a new areal radius that is time-dependent, R(t,r)=a(t)r, and a dynamical scalar coupling factor B(t). It results in a unique line element that describes all known cosmological scenarios starting from primordial inflation, followed by a radiation-dominated era, matter dominance, and ending in an accelerating Universe at late times, without appealing to a different mechanism for each phase. We resolve the Hubble tension using our dimensionless geometric coupling constant, B_0=0.1503, predict an observable spectrum of inflationary fluctuations, consistent with Planck 2018, forecast dynamical dark energy dynamics consistent with DESI 2024 observations, and provide a natural geometric solution to the formation of overmassive black holes found recently with the help of the James Webb Space Telescope. In addition, we derive an exact geometric duality between the black hole interior and the early Universe, thereby allowing us to propose singularity-resolution and information-preservation mechanisms. Six specific predictions are made, ready to be tested with upcoming experiments such as LiteBIRD, DESI, Euclid, and LISA.