Cosmology with non-linear scalar field

Mukhanov and Vikman have studied inflation model with the non-linear (NL) scalar field. We discuss the dark energy model with the Lagrangian in the presence of the square potential. We analyse the sufficient condition for the existence of an attractor solution, and compare the equation of state parameter, the present age of universe and the transition redshift with the quintessence model. We also use the Gold dataset of 157 SN-Ia to finally constrain the parameter of the models. We find that the considered model is consistent with the observation and a little inferior to the quintessence model. The above Lagrangian is similar to the non-linear Born–Infeld (NLBI) scalar field model, while which is superior to the quintessence model.