Hubble Parameter in QCD Universe for finite Bulk Viscosity

TL;DR

This paper investigates how perturbative bulk viscosity affects the evolution of the Hubble parameter during the QCD era of the early Universe, using lattice QCD data and causal thermodynamics, revealing slight deviations from ideal cosmology.

Contribution

It introduces a perturbative and numerical analysis of bulk viscosity effects on the Hubble parameter in the early Universe during the QCD epoch, based on recent lattice QCD and Israel-Stewart theory.

Findings

Viscous corrections cause slight deviations in Hubble evolution.

Numerical and perturbative approaches qualitatively agree.

Results are confined to a narrow QCD era interval.

Abstract

We consider the influence of the perturbative bulk viscosity on the evolution of the Hubble parameter in the QCD era of the early Universe. For the geometry of the Universe we assume the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker metric, while the background matter is assumed to be characterized by barotropic equations of state, obtained from recent lattice QCD simulations, and heavy--ion collisions, respectively. Taking into account a perturbative form for the bulk viscosity coefficient, we obtain the evolution of the Hubble parameter, and we compare it with its evolution for an ideal (non-viscous) cosmological matter. A numerical solution for the viscous QCD plasma in the framework of the causal Israel-Stewart thermodynamics is also obtained. Both the perturbative approach and the numerical solution qualitatively agree in reproducing the viscous corrections to the Hubble parameter, which in the viscous case turns out to be slightly different as compared to the non--viscous case. Our results are strictly limited within a very narrow temperature- or time-interval in the QCD era, where the quark-gluon plasma is likely dominant.