Quintessential inflation in mimetic dark matter -

Abstract

Quintessential inflation models have been introduced drastically in the literature to account for the existence of the cosmological constant and to combine it with inflation. It was first introduced by Einstein in an ad hoc way to account for a static behavior of the universe. Later on it was used to also try to link inflation with the later on stages of the Universe. A new quintessential inflation model is the topic of this thesis. The model will be a specific situation of the more general model called “Mimetic Dark Matter” introduced by Chamseddine and Mukhanov in 2013. It was shown in [15] that introducing a potential is essential to study the dynamics of the universe. In this thesis, the potential used will be defined on two different intervals, one before the end of inflation, and the other after it, with parameters that will be fixed in a way to produce 60 e-folds inflation and an energy density that represents a cosmological constant. The results agree with inflation during the first phase, both for the scale factor and the energy density. Moreover, an energy density will decreases like 1-t² after inflation and then converges to a constant; the constant which represents energy density of Quintessence (or Dark energy). In addition, quantum cosmological perturbations will be discussed in a way similar to that presented in [15], but the detailed calculations are not carried out in here, they will be left for future work. Finally, a comparison of the model with that given by Peebles and Vilenkin in [11] is carried out, to finish with a conclusion and potential future work to enhance the model.