Marginal IR running of Gravity as a Natural Explanation for Dark Matter

Abstract

We propose that the infrared (IR) running of Newton's coupling provides a simple and universal explanation for large-distance modifications of gravity relevant to dark matter phenomenology. Within the effective field theory (EFT) framework, we model $G(k)$ as a scale-dependent coupling governed by an anomalous dimension $\eta$. We show that the marginal case $\eta =1$ is singled out by renormalization group (RG) and dimensional arguments, leading to a logarithmic potential and a $1/r$ force law at large distances, while smoothly recovering Newtonian gravity at short scales. The logarithmic correction is universal and regulator independent, indicating that the $1/r$ force arises as the robust IR imprint of quantum-field-theoretic scaling. This provides a principled alternative to particle dark matter, suggesting that galactic rotation curves and related anomalies may be understood as manifestations of the IR running of Newton's constant.

arXiv comment11 pages, 3 figures, 2 tables; Published in Physics Letters B

References in corpus (11)

• emcee: The MCMC Hammer
• Particle Dark Matter: Evidence, Candidates and Constraints
• General relativity as an effective field theory: The leading quantum corrections
• Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature
• Dark matter and the early Universe: a review
• Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
• Indefinitely Flat Circular Velocities and the Baryonic Tully-Fisher Relation from Weak Lensing
• Rotation Curve Decomposition for Size-Mass Relations of Bulge, Disk, and Dark Halo in Spiral Galaxies
• Running of Newton's constant and non integer powers of the d'Alembertian
• Reconstructing a Model for Gravity at Large Distances from Dark Matter Density Profiles
• Dark matter or strong gravity?