  Within the scope of a LRS Bianchi type-I cosmological model we study the role
of the nonlinear spinor field in the evolution of the Universe. In doing so we
consider a polynomial type of nonlinearity that describes different stages of
the evolution. Finally we also use the observational data to fix the problem
parameters that match best with the real picture of the evolution. The
assessment of the age of the Universe in case of the soft beginning of
expansion (initial speed of expansion in a point of singularity is equal to
zero) the age was found 15 billion years, whereas in case of the hard beginning
(nontrivial initial speed) it was found that the Universe is 13.7 billion years
old.
