A Dynamical Realization of Holography in Cosmology from Hyperbolic General Relativity: Explicit Dimensional Reduction via Curvature-Generated Shock Relaxation

Holography asserts that the dynamics of a gravitational system may be determined by degrees of freedom associated with a lower-dimensional structure, rather than by independent volumetric variables. While this principle is well established in boundary-based constructions, its realization in cosmology has remained elusive due to the absence of fixed asymptotic boundaries. In this work, we present an explicit realization of holography in cosmology arising directly from the hyperbolic structure of general relativity. We show that the nonlinear evolution of the Einstein equations coupled to a scalar field generically produces a global control structure identified with the cosmological apparent horizon. By applying the Unified First Law of Thermodynamics (-dE = T\,dS) to this horizon, we obtain a geometric closure for the net exchange flux Q under the explicit assumption that the only energy exchange between the bulk and the auxiliary (unresolved) sector is mediated through the apparent-horizon screen, constraining the bulk energy density to scale as \rho \propto L^{-۲} and thereby imposing a Bekenstein-Hawking area law (S \propto A) on the bulk entropy. We demonstrate that bulk cosmological observables -- including the expansion history and late-time acceleration -- are functionals of this codimension-one structure rather than independent volumetric degrees of freedom. The construction constitutes a concrete, equation-level realization of holography in cosmology, achieved via dynamical dimensional reduction of the phase space.

کلیدواژه ها:

Cosmology ، Holography ، Dark Energy ، Hyperbolic General Relativity ، Horizon Thermodynamics ، Dimensional Reduction