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

TL;DR

The work shows that the infrared running of Newton's constant, driven by a marginal anomalous dimension η=1, generates a universal logarithmic correction to the Newtonian potential, producing a 1/r force at large scales. This IR effect is robust across regulators and can fit galactic rotation curves with a single crossover scale, while remaining compatible with BBN, CMB, and late-time cosmology for small additional energy density ΩL0. Although promising as an alternative to particle dark matter, replacing DM on all cosmological scales remains constrained by CMB observations. Overall, the paper provides a principled link between quantum gravity scaling and astrophysical phenomena, with testable predictions for lensing and structure growth.

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 $η$. 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.

Figures (3)

• Figure 1: Observed rotation curves (blue points) and best-fit tail profiles (red dashed) for three representative galaxies (700624, 700916, and 705253) from the S-sample rotation curve database of Sofue (2016) Sofue:2015tsa. The outermost velocity points (orange) are used to determine the asymptotic flat velocity $V_0$, which is then related to the IR running scale $k_\ast$ through our modified gravitational law. In each case, the outer rotation curve is well reproduced by the model with a single parameter $k_\ast$, corresponding to crossover radii in the range $36\text{--}38\,\mathrm{kpc}$ with small statistical uncertainties.
• Figure 2: Corner plot showing the marginalized posterior distributions and covariances for $\Omega_{\mathrm{m0}}$, $H_0$, and $\Omega_{L0}$ obtained from the $H(z)$ dataset (38 data points from Ref. Farooq:2016zwm). Dashed vertical lines indicate the 16th, 50th, and 84th percentiles. The filled contours correspond to the $1\sigma$ (68%), $2\sigma$ (95%), and $3\sigma$ (99.7%) credible regions, respectively. A mild degeneracy between $\Omega_{\mathrm{m0}}$ and $H_0$ is visible, while $\Omega_{L0}$ is largely uncorrelated with the other parameters. The latter is entirely expected for a new, sub-dominant physical effect.
• Figure 3: Observed $H(z)$ data points (blue) with $1\sigma$ error bars, along with the best-fit model curve (orange) corresponding to the median parameter values in Table \ref{['tab:bestfit_params']}. The model provides an excellent fit to the background expansion history over the entire observed redshift range.