  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.
