Renormalization Group Approach to Causal Viscous Cosmological Models

TL;DR

This paper applies the renormalization group method to analyze homogeneous, flat cosmological models with causal bulk viscous fluids, deriving conditions for scale invariance and long-term behavior of the universe.

Contribution

It introduces a novel application of the renormalization group approach to causal viscous cosmology, establishing scale invariance constraints and analyzing the universe's evolution.

Findings

Derived scale invariance constraints on viscosity, temperature, and relaxation time.

Identified the long-term behavior of the scale factor near the fixed point.

Analyzed the flow for viscosity proportional to the Hubble parameter.

Abstract

The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, of the causal evolution equation of the bulk viscous pressure and of the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale invariant fixed point, therefore obtaining the long time behavior of the scale factor.