On the Admissible Magnitude of the Effective Acceleration-Driving Contribution in Relativistic Cosmology

While the timing of late-time cosmic acceleration is shown to be a structural necessity of relativisticcosmological dynamics, the observed magnitude of the effective acceleration-driving contribution iscommonly regarded as unnatural or fine-tuned.In this work, we demonstrate that the smallness of the effective acceleration scale does not requiremicrophysical explanation at the level of background cosmology and does not constitute a dynamicalcoincidence. Instead, we show that values of the effective acceleration-driving contribution substantially larger or smaller than the observed one are either empirically excluded, dynamically irrelevant,or observationally indistinguishable.We prove that the observed magnitude corresponds to a narrow admissible window defined bythree independent structural requirements: the existence of a prolonged matter-dominated era, thenecessity of late-time dominance of the acceleration-driving contribution, and the requirement thatthe transition to acceleration occur within the observable cosmic history.This result reframes the cosmological constant problem as a question of microscopic origin ratherthan macroscopic admissibility and completes the structural closure initiated in the first article ofthis series. Structural Explanation of Late-Time Cosmic Acceleration A Three-Paper Series in Relativistic Cosmology This research program presents a model-independent, structurally closed explanation of late-time cosmic acceleration within the framework of relativistic cosmology. The series consists of three tightly connected articles, each addressing a logically distinct aspect of the phenomenon. Rather than proposing new dynamical fields, modified gravity models, or speculative microphysics, the series identifies those features of cosmic acceleration that are already fixed by general covariance, cosmological history, and observational accessibility. Article I Late-Time Cosmic Acceleration as a Structural Necessity of Relativistic Cosmology The first article establishes that the timing of late-time cosmic acceleration is not contingent or model-dependent. Under minimal assumptions—spatial homogeneity and isotropy, general covariance, conservation of the energy–momentum tensor, and the existence of a prolonged matter-dominated era—the transition from decelerated to accelerated expansion is forced to occur at redshift of order unity. This result closes the logical space of explanations for when acceleration begins. Article II On the Admissible Magnitude of the Effective Acceleration-Driving Contribution in Relativistic Cosmology The second article addresses the long-standing question of the magnitude of the acceleration-driving contribution. It demonstrates that values substantially larger or smaller than the observed one are either empirically excluded, dynamically irrelevant, or observationally indistinguishable. The observed magnitude is shown to lie within a narrow admissible window defined by structural constraints rather than microphysical tuning, reframing the cosmological constant problem as a question of microscopic origin rather than macroscopic admissibility. Article III Why the Vacuum Scale Tracks the Cosmological Horizon: Structural Constraints from Covariance and Observability The third article explains why the effective vacuum scale relevant for cosmic acceleration tracks the cosmological horizon. It is shown that any gravitationally active vacuum contribution compatible with cosmic history must be infrared-dominated and covariant, leaving the Hubble scale as the unique admissible geometric scale. This result closes the remaining conceptual gap between vacuum physics and cosmological acceleration. Structural Closure Together, the three articles provide a complete, internally consistent, and model-independent explanation of late-time cosmic acceleration at the level of relativistic cosmology: Article I: inevitability of timing Article II: admissible magnitude Article III: horizon-scale origin The series establishes which aspects of cosmic acceleration are structurally fixed and which questions remain genuinely open at the level of microscopic physics.