Scenarios of the cosmological evolution are studied by using an equation of state (EoS) having points where the specific enthalpy of the cosmological fluid vanishes. A large class of barotropic EoS's admits, depending upon initial conditions, analogues of the "Big Rip", as well as solutions describing exponential inflation followed by usual matter dominance; their classification is proposed. We discuss extensions to more general two-parametric EoS dealing with a pre-inflationary evolution and yielding stages with both increasing and decreasing energy density as a function of time. Possible cosmological scenarios with transitions from collapse to an expanding Universe or a closed oscillating one, without reaching a singularity are included.