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

Abstract

We study coherent aggregates of orientation-reversed contributions in the spectrum of the Loop Quantum Gravity (LQG) volume operator and investigate their possible coarse-grained statistical description. These configurations correspond to sectors of the kinematical Hilbert space where orientation-dependent contributions to the volume operator change sign. We develop an effective description in which cosmic evolution is governed by a dynamical redistribution between positive and negative orientation sectors. In this phenomenological picture, the macroscopic expansion of space can be modeled as an emergent phenomenon aris- ing from the gradual conversion of latent geometric capacity into positive-volume-dominated configurations, mediated by domain-wall-like structures in the orientation field. An effective statistical model based on an Ising-like representation of vertex orientations is introduced to describe the coarse-grained dynamics of LGRs. This leads to modified Friedmann equations with an additional time-dependent contribution that behaves similarly to dark energy at the background level. We derive the associated dynamical system and identify the relevant dimensionless parameters governing the conversion process. The framework yields phenomenological implications for cosmological observables, in- cluding late-time expansion history and possible signatures in gravitational wave spectra and quantum geometric simulations. However, we emphasize that these predictions depend on an effective coarse-graining of LQG dynamics and should not be interpreted as direct consequences of a complete quantum gravitational theory. The work is intended as a kinematically grounded but phenomenological extension of LQG, aiming to explore whether orientation-sector dynamics can provide an alternative interpretation of dark-energy-like behavior. 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, and outline a set of observational probes that could constrain or falsify the effective framework.

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