Geometric Annihilation and Cosmic Acceleration: Cosmological Signatures of Latent Geometric Regions

Abstract

This work proposes a physically grounded framework for cosmic expansion based on the concept of Latent Geometric Capacity within Loop Quantum Gravity (LQG). We distinguish between space—the pre-geometric capacity for adjacency and volume—and the universe—the actually occupied classical volume. In LQG spin networks, a connected cluster of vertices with inverse orientation (μ_v = -1) constitutes a Latent Geometric Region (LGR): a topological defect in the orientation field that contributes negatively to the volume operator. An isolated μ_v = -1 vertex remains a gauge artifact. Cosmological expansion is modeled as geometric annihilation: the dynamical conversion of latent capacity into positive classical volume at the interface between actualized (V_+) and latent (V_-) domains. The effective 4D dynamics are governed by the Einstein equations supplemented by an energy-momentum tensor sourced by the domain wall. We present an explicit analytical calculation of the volume operator on a minimal tetrahedral spin-network graph (all spins j = 1/2), demonstrating exact cancellation of volume when one vertex is inverted. An effective Ising-like Hamiltonian describes the large-scale orientation dynamics, enabling a statistical estimate of the macroscopic latent fraction. The framework yields falsifiable predictions for (i) oscillatory features in the primordial power spectrum at high multipoles, (ii) fractional shifts in quasinormal mode frequencies of binary black hole mergers, and (iii) negative expectation values of the volume operator in few-qubit quantum simulations. We perform a detailed comparison with recent cosmological data (Planck 2018, DESI DR2) and outline a phased research roadmap. This paper builds upon the Latent Geometric Region framework introduced in a companion paper (AL_78, "Latent Geometric Regions: A Heuristic Framework for Capacity-Driven Cosmic Expansion," in preparation, 2026). The primary contribution is conceptual and interpretative, but is anchored to a tractable computational core. The framework offers a novel perspective on cosmic expansion as the progressive actualization of pre-geometric potential.

Keywords