A Late-Time Scalar Modulation of Cosmic Expansion: Implications for the Hubble Tension

This work presents a minimal effective-field extension of standard cosmology aimed at addressing the Hubble tension, the persistent discrepancy between early- and late-universe determinations of the Hubble constant. We introduce a late-time scalar degree of freedom, denoted as (x^), phenomenologically coupled to the matter sector, which modulates the expansion history of the Universe. In this framework, the effective Hubble parameter acquires both temporal and weak environmental dependence, allowing different observational regimes to infer distinct values of H₀ without requiring inconsistencies in the underlying cosmological model. The model is formulated at the level of the action, with derived field equations, modified Friedmann equations, and explicit energy exchange terms between matter and the scalar sector. A dynamical system formulation is also developed to analyze the cosmological evolution, including the identification of fixed points and late-time attractors. Numerical integration and illustrative expansion histories demonstrate that the scalar-modulated model produces controlled deviations from CDM at late times while preserving the behavior of the early Universe. The resulting expansion history naturally shifts the inferred value of H₀ toward the range indicated by local measurements, providing a regime-dependent interpretation of the Hubble tension. The framework remains minimal, testable, and compatible with current observational constraints from Planck, Type Ia supernovae, baryon acoustic oscillations (BAO), and strong-lensing time-delay cosmography. A possible connection with the broader ToE-2PS (Theory of Everything in Phase Space) program is discussed as a theoretical extension, while all results are derived within a standard effective-field-theory approach. Overall, this work proposes a coherent and falsifiable late-time cosmological mechanism capable of reconciling current observational tensions in precision cosmology.