From the Planck Horizon to the Cosmic Scale: Emerging Local Acceleration as a Conformal Holographic Constraint

This study introduces a fundamental ontological paradigm shift aimed at resolving the structural discrepancy between General Relativity and Quantum Mechanics, while providing a formal solution to the "vacuum catastrophe." We propose moving beyond the standard expanding spacetime model in favor of a framework characterized by the metric invariance of global spacetime, interpreted as a stationary, saturated geometric-hydrodynamic continuum. Within this static background metric, cosmological dynamics are redescribed—via a conformal transformation governed by a dilaton scalar field—as the progressive, accelerated contraction of local atomic reference frames (matter).The logical center of this model relies on a pure kinematic scale-coupling equation, $a_{\text{local}} = \sqrt{a_{\text{cosm}} \times a_{\text{Planck}}}$, defined as the exact conformal projection and holographic constraint mapping the information flux between the two-dimensional (2D) cosmic horizon and the three-dimensional (3D) volume of matter. To eliminate logical circularity, the hadronic density parameter $\rho_0 = 10^{35} \text{ J/m}^3$ is elevated to a fundamental hydrodynamic tensor constant, defining the bulk modulus of spacetime. From this constant, we analytically derive the Tollini kinematic limit acceleration ($a_T = c^2/r_p \approx 1.197\times 10^{31} \text{ m/s}^2$) independently of Newton’s gravitational constant ($G$).We demonstrate that macroscopic gravity is not an independent fundamental force but an emergent property arising from the geometric scaling of maximum quantum acceleration, wherein $G$ emerges as a parameter derived from the ultraviolet interface of the vacuum. This configuration resolves the 120-order-of-magnitude discrepancy of the cosmological constant, as zero-point fluctuations are naturally confined by the hydrodynamic potential of the medium, excluding macroscopic gravitational self-interactions in the absence of density gradients. Finally, the model’s compatibility with stringent local experimental constraints on atomic constant stability (e.g., Oklo natural reactor data) is ensured by introducing a Chameleon-type effective screening potential. In high-baryon-density regimes, the scalar field is "frozen," locally halting contraction and preserving proper Lorentz Invariance, while manifesting freely in intergalactic voids to account for the observed redshift ($z$) as a scale variation of the observer’s measuring rods.Keywords: Conformal Invariance, Hydrodynamic Spacetime, Emergent Gravity, Holographic Principle, Chameleon Mechanism, Vacuum Catastrophe.