Infrared Running of Newton’s Coupling Explains Dark Matter with Logarithmic Force Laws

The persistent mystery of dark matter receives a novel explanation in new research exploring how gravity itself might behave over vast cosmic distances. Naman Kumar, from the Indian Institute of Technology Gandhinagar, and colleagues propose that gravity’s strength isn’t constant, but subtly changes with distance, a phenomenon known as infrared running. This work demonstrates that a specific mathematical case, where the change is marginal, naturally leads to a force law differing from Newton’s at large scales, potentially accounting for the observed rotation of galaxies without invoking new particles. The team’s approach offers a compelling alternative to traditional dark matter theories, suggesting that the anomalies currently attributed to unseen matter may instead arise from the fundamental way gravity operates across the universe.

The research demonstrates that the marginal case η = 1 is uniquely identified by renormalization group (RG) and dimensional arguments, resulting in a logarithmic potential and a 1/r force law at large distances. Simultaneously, the approach smoothly recovers Newtonian gravity at short scales, indicating a universal and regulator-independent logarithmic correction. This suggests the 1/r force arises as a robust infrared (IR) imprint of quantum-field-theoretic scaling, offering a principled alternative to particle dark matter. The investigation proposes that galactic rotation curves and related anomalies may be understood as manifestations of the IR running of Newton’s constant, addressing one of the most persistent puzzles in modern physics, namely the nature of dark matter.

Running Newton’s Constant and MOND Emergence

This work presents a comprehensive exploration of modified Newtonian dynamics (MOND) and the possibility of explaining dark matter effects through a running Newton’s constant within the framework of quantum field theory and effective field theory. The central hypothesis is that Newton’s gravitational constant (G) is not constant, but varies with energy scale, linked to the renormalization group flow in a quantum field theory of gravity. This research positions MOND not as a fundamental theory, but as an effective description arising from this running G, providing a theoretical underpinning beyond purely phenomenological adjustments. The running G is proposed as a mechanism to explain the observed flat rotation curves of galaxies without invoking dark matter, effectively mimicking the effects usually attributed to unseen mass.

The work emphasizes treating gravity as an effective field theory, focusing on low-energy behavior and incorporating quantum corrections systematically. This approach offers a pathway toward a more fundamental description, as the scale at which G runs could be related to the Planck scale or other fundamental parameters. The use of retarded solutions in the nonlocal gravity construction ensures that the theory respects causality, a crucial requirement for any physical theory. This approach is theoretically motivated, utilizes a powerful and well-established technique, and attempts to answer why MOND works, rather than simply that it works. Future research should determine the energy scale at which G runs, investigate the cosmological implications for the early universe, and explore whether this model can explain galaxy formation and large-scale structure without dark matter. Further investigation is needed into lensing effects, connections to quantum gravity theories, and specific experiments to test the predictions of this model, such as precision measurements of gravity at different scales.

Logarithmic Gravity Explains Galactic Rotation Curves

Scientists have discovered a compelling explanation for observed galactic rotation curves and related anomalies, proposing that modifications to Newton’s law of gravity, rather than dark matter, may account for these phenomena. Their research demonstrates that the infrared behavior of Newton’s coupling, essentially how gravity behaves over vast distances, undergoes a predictable “running,” altering the gravitational force at large scales. The team modeled this behavior within an effective field theory framework, revealing that an anomalous dimension governs the scale-dependent coupling. The results show that a specific, “marginal” case, where the anomalous dimension equals one, is uniquely favored by both renormalization group and dimensional arguments, leading to a logarithmic potential and a resulting 1/r force law at large distances.

This modified force law supports recent findings that galactic rotation curves remain flat indefinitely. The team’s approach provides a principled, model-independent motivation for exploring these infrared modifications to gravity, deriving the altered force law as a natural consequence of the running of Newton’s constant. Experiments reveal that this 1/r force is analogous to how quantum field theory couplings behave at critical points, suggesting that spacetime effectively has reduced dimensionality in the infrared. The research demonstrates that the flattening of galactic rotation curves may be understood as a macroscopic manifestation of this quantum-field-theoretic running of Newton’s coupling.

By promoting Newton’s constant to a spacetime-dependent scalar, the team constructed modified Einstein equations and investigated spherically symmetric spacetimes, showing that specific power-law runnings of this constant could lead to non-Keplerian rotation curves without invoking dark matter halos. Furthermore, the team’s analysis singles out a unique marginal running of Newton’s coupling, corresponding to an anomalous dimension of one, as the only scale-invariant deformation consistent with rotational symmetry and locality in time. The resulting potential is logarithmic, and the team derived a force law that, at distances greater than 1/k∗, is dominated by a 1/r term, offering a consistent and compelling alternative to dark matter explanations for observed galactic dynamics.

Logarithmic Gravity Arises From Infrared Running

The research demonstrates that the infrared (IR) running of Newton’s coupling, essentially how the strength of gravity changes with distance, provides a natural explanation for modifications to gravity at large distances. By treating the gravitational constant as scale-dependent within an effective field theory, the team found that a specific anomalous dimension singles itself out, leading to a logarithmic potential and a resulting 1/r force law at large distances, while smoothly reverting to Newtonian gravity at shorter ranges. This logarithmic correction is notably universal, being independent of the specific ultraviolet regulator used in calculations, which suggests its robustness as a prediction of quantum field theory. This work offers a new approach to understanding phenomena currently attributed to dark matter, such as the observed flattening of galactic rotation curves.

Unlike models that propose new particles or modify gravity empirically, this framework derives the modification from the renormalization group flow itself, suggesting galactic rotation curves may be a macroscopic manifestation of infrared scaling in quantum gravity. The authors acknowledge that further investigation is needed to quantitatively assess the viability of this 1/r force as an alternative to dark matter, and to embed this running within more complete frameworks of quantum gravity. Future research directions include confronting the model with astrophysical data at galactic and cluster scales, exploring cosmological implications for structure formation and lensing, and deriving the crossover scale from a more fundamental theory. In conclusion, the IR running of Newton’s coupling presents a simple, universal, and theoretically well-motivated modification of gravity, offering a promising new perspective on the dark matter problem.