Abstract
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.
Highlights
Based on observations [1,2,3], we can say that the universe today is almost flat
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 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
Summary
Based on observations [1,2,3], we can say that the universe today is almost flat. If this is the case, i.e., it has remained flat since the beginning of time? To this problem of flatness, we can add the horizon problem. This work is based on an article published in 1974 by [5] followed by [6] where they show that only four families of terms lead to a violation of the equivalence principle, while ensuring to obtain the equations of motion of the second member. These couplings are given in [6] as the “Fab Four”. We consider a Lagrangian with two parts: the first is the non-minimal derivative coupling of the form
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