On Meta-Geometric Gravity, Emergent Holography and Naturalness.

Abstract

We show that a discrete quantization law for cosmological entropy emerges naturally within a meta-geometric gauge theory of gravity, when the standard de Sitter entropy relation is combined with the topological structure of the theory. Our framework is based on a pre-metric action containing a MacDowell-Mansouri term with a spontaneously broken (A)dS gauge symmetry reduced to the Lorentz subgroup. We derive an inverse proportionality between the topological θ-angle and the cosmological constant, which enforces a topological quantization condition. As a consequence, the de Sitter entropy becomes quantized and scales linearly with a topological quantum number. This quantization provides a natural entropic stabilizer and a quantum topological protection for a large cosmological constant, thereby offering a microscopic gauge-theoretic realization of the holographic naturalness conjecture. We also discuss possible emergence of the N-portrait in cosmology and a dynamical relaxation of the vacuum energy.