Universal properties of the evolution of the Universe in modified loop quantum cosmology

In this paper, we systematically study the evolution of the Universe in the framework of a modified loop quantum cosmological model (mLQC-I) with various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T- models and natural inflation. In all these models, the big bang singularity is represented by a quantum bounce, and the evolution of the Universe both before and after the bounce is universal and weakly depends on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the evolution in the pre-bounce region can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, w = 1. Soon, the inflation potential takes over, so w rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant with a Planck size takes over and dominates the rest of the contracting phase. In the entire pre-bounce regime, the evolution of the expansion factor and the inflaton can be approximated by analytical solutions, which are universal and independent of the inflation potentials.