Cosmological models with modified equations of state for dark energy

We consider cosmological scenarios which generalize the well-known $\Lambda$CDM and $w$CDM models and have the equations of state $p_x=w(a) \rho_x$ and $p_x=f(\rho_x)$ for dark energy. Here the factor $w(a)$ can depend on the scale factor $a$, $p_x$ and $\rho_x$ are dark energy pressure and density respectively. We analyze these models comparing their predictions with observational data for type Ia supernovae, the Hubble parameter $H(z)$ and baryon acoustic oscillations. From this point of view we obtain and investigate the most successful model $w(a)=w_0+w_1(1-a)^3$ among the considered scenarios.