Super inflation mechanism and dark energy in $F(T,T_{G})$ gravity

Abstract

There are various mechanisms that explain both the inflationary epoch of the early universe and a unification of this epoch with the other stages of the universe. In this study, we show all the expansion history of the universe and transition among of them in a single form by using the theoretical framework of $F ( T, T_{G} )$ gravity in the context of the FRW (Friedmann-Robertson-Walker) universe. According to a particular model we obtain the unified solutions of the field equations. Without using any scalar field description we especially present the super inflation mechanism composed of three phase regions which describes the evolution of the early universe. The mechanism begins with a vacuum state and then follows a super accelerated period where there are two regions. The first continues in a quintessential field, and the second is a region where the radiation is created. Furthermore, we verified this inflationary mechanism by using the spectral index parameter and the scalar tensor ratio, i.e., $n_{s}$, $r$, and calculated the ratio of radiation emergent from the quintessence field. This creation should be in a certain rate in the early universe otherwise we show that the universe cannot survive and continue to expand. Also, we have obtained a phantom solution of the model that shows two regions which are compatible with the recent cosmological observations. In one respect, it is observed that the late time expansion of the universe is similar to the early time inflation.