Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves

TL;DR

This paper explores how quantum gravity effects, modeled through a renormalization group approach, can modify Newton's constant and potentially explain galaxy rotation curves without dark matter.

Contribution

It introduces a RG-improved Einstein-Hilbert action with spacetime-dependent constants and applies it to galaxy rotation curves, offering a novel quantum gravity explanation.

Findings

RG modifications can produce non-Keplerian galaxy rotation curves

A small power-law running of Newton's constant explains flat rotation curves

No dark matter needed in the model to fit galactic dynamics

Abstract

A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a ``cutoff identification'' which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, static spacetimes are derived and analyzed in detail. The modifications of the Newtonian limit due to the RG evolution are obtained for the general case. As an application, the viability of a scenario is investigated where strong quantum effects in the infrared cause Newton's constant to grow at large (astrophysical) distances. For two specific RG trajectories exact vacuum spacetimes modifying the Schwarzschild metric are obtained by means of a solution-generating Weyl transformation. Their possible relevance to the problem of the observed approximately flat galaxy rotation curves is discussed. It is found that a power law running of Newton's constant with a small exponent of the order $10^{-6}$ would account for their non-Keplerian behavior without having to postulate the presence of any dark matter in the galactic halo.