Cosmological dynamics of gravitating hadron matter

Anisotropic cosmologies are studied in the case where the matter source is given by the Skyrme model which is an effective description of low energy QCD. The dynamical evolution of the Kantowski-Sachs and Bianchi-I universes are analyzed in depth. In both situations in order for solutions to exist and at the same time to avoid finite time future singularities, bounds on the value of the cosmological constant and on the values of the Skyrme couplings must be set. The upper bound on the cosmological constant, which depends also on the initial conditions is closely related to the fact that the baryons appear below 1 GeV. The upper bound on the cosmological constant is actually 72 orders of magnitudes lower than the standard estimations from quantum field theory. The lower bound on the cosmological constant and the bounds on the Skyrme couplings are due to the peculiar combination of nonlinear terms in the Skyrme model. It is worth to point out that bounds on the Skyrme couplings occur in similar fashion both for the Kantowski-Sachs and for the Bianchi-I models which are topologically completely different. Our results suggest that this behavior is intrinsic to the coupling of the Skyrme field to gravity rather than on a specific cosmological model.