  We investigate cosmological consequences of nonlinear sigma model coupled
with a cosmological fluid which satisfies the continuity equation. The target
space action is of de Sitter type and is composed of four scalar fields. The
potential which is a function of only one of the scalar fields is also
introduced. We perform a general analysis of the ensuing cosmological equations
and give various critical points and their properties. Then, we show that the
model exhibits exact cosmological solution which yields a transition from
matter domination into dark energy and compare it with the $\Lambda$CDM
behavior. Especially, we calculate the age of the Universe and show that it is
consistent with the observational value if the equation of the state $\omega_f$
for the cosmological fluid is within the range of $0.13 < \omega_f < 0.22.$
Some implication of this result is also discussed.
