Renormalization group scale-setting in astrophysical systems

TL;DR

This paper introduces a generalized scale-setting method for applying Renormalization Group corrections in General Relativity, with applications to astrophysical systems and galaxy rotation curves.

Contribution

It proposes a new, more general scale-setting procedure for RG corrections in GR and applies it to symmetric systems, matching galaxy rotation curve explanations.

Findings

Analytical scale-setting for polytropic systems

Matching of the scale with previous galaxy rotation models

Potential to systematically explain galaxy rotation curves

Abstract

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the renormalization group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this paper is identified as an important future goal.