Chaplygin Gas models without Chaplygin Gas EoS

The equation of state of Chaplygin Gas is one of the simplest ways to illustrate dark energy effects during the late time. Indeed, while one uses the equation of state of Chaplygin Gas, the continuity equation gives specific energy density which satisfies both deceleration (matter dominated) and acceleration (dark energy epoch). In other words, for the earlier universe, the energy density of whole energy-matter component behaves as matter era (baryonic and dark matter) and treats such as dark energy in the standard model of cosmology Lambda-CDM when a goes to infinity. Here, by using the general form of F(R) gravity while the pressure of matter is non-zero, we show that even for Einstein gravity (GR), one obtains a viable cosmological model with the same energy density of Chaplygin Gas while Chaplygin Gas EoS is not used. Further, we investigate cosmic evolution through two other different forms of F(R) gravity and show general behavior of Hubble parameter, cosmological scale factor and equation of state throughout cosmic time.