Marginal IR running of gravity as a natural explanation for dark matter

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 η . We show that the marginal case η = 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.