Renormalization Group Calculation of the Galaxy-Galaxy Correlation Function

TL;DR

This paper applies renormalization group techniques to a scalar field theory model of galaxies, predicting the galaxy-galaxy correlation function and its critical exponent, bridging cosmological observations with statistical physics methods.

Contribution

It introduces a novel approach using Ising model mapping and renormalization group analysis to calculate galaxy correlation functions.

Findings

Predicted critical exponent between 1.530 and 1.862

Correlation function aligns with observed phenomenological range

Established a theoretical framework linking cosmology and critical phenomena

Abstract

The observable Universe is described by a collection of equal mass galaxies linked into a common unit by their mutual gravitational interaction. The partition function of this system is cast in terms of Ising model spin variables and maps exactly onto a three-dimensional stochastic scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, compared to the phenomenological value of 1.6 to 1.8