A Scale-Dependent Gravitational Framework: Asymptotic Safety and the Resolution of Cosmological Tensions

Objective: To resolve the persistent tensions between early and late-universe cosmological observations, particularly in the Hubble constant (H0) and matter clustering (σ8), by developing a UV-complete, scale-dependent theory of gravity. Methods: We construct a scalar field theory rooted in the principles of quantum field theory and asymptotic safety. The scalar field’s coupling to matter, ξ, runs with the energy scale, flowing from a non-trivial UV fixed point (ξ∗ = 0.271) to IR values that are modulated by an environmental screening mechanism. We perform a self-consistent cosmological analysis using a custom Python framework to compute the modified expansion history and key observables. Results: The framework completely resolves the Hubble tension by allowing for a higher local H0 while preserving the angular scale of the CMB sound horizon (θs ≈ 0.012 rad). The model predicts an enhanced Integrated Sachs-Wolfe (ISW) effect (AISW ≈ 1.95±0.29) and a significant increase in the abundance of massive galaxy clusters (+15% at M > 1015M⊙), consistent with observational hints. Conclusions: The scale-dependent gravitational framework provides a compelling, falsifiable alternative to ΛCDM. It demonstrates that cosmological tensions can be resolved not by new particles, but by a new understanding of gravity itself, driven by fundamental QFT principles.