Why the Vacuum Scale Tracks the Cosmological Horizon: Structural Constraints from Covariance and Observability

ABSTRACT We present a model-independent structural theory of late-time cosmic acceleration. We provethat (i) the timing of the transition to accelerated expansion, (ii) the admissible magnitude of theeffective acceleration-driving contribution, and (iii) the tracking of the vacuum scale to the cosmological horizon are not contingent features of microphysical models but unavoidable consequencesof generally covariant cosmological dynamics combined with empirical boundary conditions. Theresults close the explanatory space of late-time acceleration at the level of relativistic cosmology andshift the remaining open problem entirely to the domain of microscopic vacuum structure.Late-time cosmic acceleration is commonly interpreted as evidence for new dynamical degrees of freedom, finelytuned parameters, or modifications of gravitational physics. In this series-synthesis work, we demonstrate that neitherthe timing, nor the magnitude, nor the characteristic scale of cosmic acceleration is contingent on microphysical modelbuilding.Instead, we show that accelerated expansion is a structural inevitability of generally covariant cosmological dynamics once three empirically established conditions are imposed: the existence of a prolonged matter-dominated era,covariant conservation of energy–momentum, and the finite observational accessibility of cosmic history.We prove that the transition to acceleration must occur at redshift of order unity, that the effective accelerationdriving contribution is constrained to a narrow admissible window around the present matter density, and that anygravitationally active vacuum contribution compatible with cosmic history must track the cosmological horizon scale.These results are independent of the microscopic origin of the vacuum sector.Together, they provide a closed, model-independent explanation of late-time cosmic acceleration within relativisticcosmology, reframing the cosmological constant problem as a question of microscopic origin rather than macroscopicadmissibility. INTRODUCTION The discovery of late-time cosmic acceleration represents one of the most profound empirical findings in moderncosmology. Despite its observational robustness, the phenomenon continues to be framed as conceptually anomalous,often attributed to unknown forms of energy, fine-tuned parameters, or infrared modifications of gravity.Three closely related questions have dominated the discussion: why acceleration begins only after a prolongedmatter-dominated era, why its effective magnitude is extraordinarily small in microscopic units, and why the relevantvacuum scale tracks the present cosmological horizon.Most existing approaches treat these features as contingent outcomes of specific dynamical models. In contrast, theQuantum Model of the Universe (QMU) program adopts a structurally constrained perspective, asking which featuresof late-time acceleration are already fixed by the architecture of relativistic cosmology itself.This work synthesizes three complementary results demonstrating that the timing, magnitude, and horizon trackingof cosmic acceleration are not optional model-dependent features, but unavoidable consequences of general covariance,cosmic history, and observational consistency.