Lagrangian formulation and implications of barotropic fluid cosmologies

In this paper, we investigate the behavior of cosmologies in homogeneous and isotropic background with a barotropic fluid. We solve the continuity equation and study several aspects of model including behavior of cosmological quantities like Hubble parameter, deceleration parameter, equation of state parameter along with statefinder diagnostic and validity of energy conditions. The gamma'-gamma plane is checked for identification of thawing and freezing regions. We derive the Lagrangian formulation with standard and non-standard kinetic terms for barotropic, fluid model. It is demonstrated that the model possesses periodic potential in its Lagrangian description with standard kinetic terms. Using dynamical system analysis, we find the stability of solutions, too. We further explore the thermodynamic aspects at apparent horizon by investigating the validity of generalized second law of thermodynamics with equilibrium description. The model exhibits complete cosmological scenario for different values of model parameters and the inflationary scenario decays smoothly into radiation-dominated phase during its evolution. The model approaches to A cold dark matter model during late times of its evolution.