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