Abstract:
In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework
of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is
categorized into two classes, first one is dominated by kinetic energy and second one by potential
energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained
numerically that generate the desired slow-roll inflation and also sufficient number of e-folds. To be
consistent with observations at least 60 e-folds are required. In case of kinetic energy dominated
(KED) initial conditions of inflaton field at the bounce, the numerical evolution of the background
prior to preheating is divided into three different regions: bouncing, transition and slow-roll inflation
whereas bouncing and transition phases disappear in the potential energy dominated (PED) case
but still slow-roll inflation is achieved. This is true in case of KED (except subset) and PED initial
conditions for p = 4 and v = 1MP l of Hilltop potential. However for other cases, slow-roll inflation
can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss
the phase space trajectories under the chosen parameters.
