Dynamics of gravitating hadron matter in Bianchi-IX cosmological model

TL;DR

This paper analyzes the dynamics of gravitating hadron matter in a Bianchi-IX cosmological model, revealing various regimes depending on parameters and the cosmological constant, with stability properties of solutions.

Contribution

It provides an analytical and semi-analytical description of asymptotic and generic regimes in the Einstein-Skyrme Bianchi-IX model, including effects of the cosmological constant.

Findings

Three regimes without cosmological term depending on K: recollapse, /2 power-law, and linear growth.

Positive B4 leads to exponential (de Sitter) regimes, recollapse can also become exponential with large B4.

Negative B4 causes recollapse regardless of K.

Abstract

We perform an analysis of the Einstein-Skyrme cosmological model in Bianchi-IX background. We analytically describe asymptotic regimes and semi-analytically -- generic regimes. It appears that depending on the product of Newtonian constant $\kappa$ with Skyrme coupling $K$, in absence of the cosmological term there are three regimes possible -- recollapse with $\kK < 2$ and two power-law regimes -- $\propto t^{1/2}$ for $\kK=2$ and $\propto t$ for $\kK > 2$. In presence of the positive cosmological term, power-law regimes turn to exponential (de Sitter) ones while recollapse regime turn to exponential if the value for $\Lambda$-term is sufficiently large, otherwise the regime remains recollapse. Negative cosmological term leads to the recollapse regardless of $\kK$. All nonsingular regimes have the squashing coefficient $a(t) \to 1$ at late times, which is associated with restoring symmetry dynamics. Also all nonsingular regimes appear to be linearly stable -- exponential solutions always while power-law for an open region of initial conditions.