Dynamics of gravitating hadron matter in Bianchi-IX cosmological model

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.