Inflation Playing by John Lagrangian

Abstract

Our goal is to reproduce in fl ation through the coupling between the non-minimal fi rst derivative of the scalar fi eld and the Einstein tensor in which we introduced a potential. We analyse the in fl ation by examining the equation of state, the expansion parameter and the scale factor. We have shown that when the potential is proportional to the fi eld φ and proportional to the square of the fi eld, in fl ation does not appear; but when the potential is an exponential function of the scalar fi eld, this model brings up in fl ation. In fl ation does not occur when the time t is near minus in fi nity but it is noticed a few units of Planck time .