Exact solution and exotic fluid in cosmology

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 $\mathrm{\Lambda }$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 $0.13<{\omega }_f<\mathrm{0.22.}$ Some implication of this result is also discussed.