Cosmological models with integrable equations of state

We consider a class of cosmological models with two components of matter in the Universe, which denoted as dust matter and dark energy. We investigate various equations of state for dark energy, which allow analytical dependence of its density $\rho_d$ on the scale factor $a$ or redshift. In comparison with the standard model $\Lambda$CDM we study its generalization $w$CDM with the dependence $\rho_d\sim a^{-3B}$, and also suggest a new equation of state with the dark component density $\rho_d=const/(A+a^{3B})$. For this class of models we estimated optimal values of the parameters and limitations on their acceptable deviations from the best description of observational data for type Ia supernovae, baryon acoustic oscillations and the Hubble parameter $H(z)$ estimations. The scenario with the new equation of state appears to be the most successful in minimization of the function $\chi^2$ measuring correspondence between a model and an observational data, however the small number of parameters makes the $\Lambda$CDM model more effective from the point of view of the Akaike information criterion.