Exploring the pre-inflationary dynamics in loop quantum cosmology with a DBI scalar field

Loop quantum cosmology is a symmetry-reduced application of loop quantum gravity. The theory predicts a bounce for the universe at the Planck scale and resolves the singularity of standard cosmology. The dynamics is also governed by an effective Hamiltonian, which predicts a modified Friedmann equation containing the quadratic terms of the energy density. The term plays an essential role in the high energy regime, but the equations return to the standard form in the low energy regime. The evolution of the universe in the pre-inflationary period is studied in the framework of loop quantum cosmology, where the DBI scalar field is assumed to be the dominant component of the universe. Using the numerical method, we provide the evolution of the DBI field. The background evolution shows that there are three phases as: bouncing phase, transition phase and slow-roll inflationary phase. There is also a short period of super-inflation just at the beginning of the bounce phase. The field first climbs the potential and then reaches the turning point where $\dot{\phi}$ disappears and the potential energy becomes the dominant part of the energy density. This is the time when the slow roll inflation begins and the field slowly rolls down the potential. The results indicate that there are a few e-fold expansions in the bounce phase, about $N = 3.5-4$, and the universe experiences about $N = 59$ e-fold expansions in the slow-roll inflation phase.