Pre-inflationary universe in loop quantum cosmology
  The evolutions of the flat FLRW universe and its linear perturbations are
studied systematically in the dressed metric approach of LQC. When it is
dominated by the kinetic energy of the inflaton at the quantum bounce, the
evolution of the background can be divided into three different phases prior to
the preheating, {\em bouncing, transition and slow-roll inflation}. During the
bouncing phase, the evolution is independent of not only the initial
conditions, but also the inflationary potentials. In particular, the expansion
factor can be well described by the same exact solution in all the cases
considered. In contrast, in the potential dominated case such a universality is
lost. It is because of this universality that the linear perturbations are also
independent of the inflationary models and obtained exactly. During the
transition phase, the evolutions of the background and its linear perturbations
are found explicitly, and then matched to the ones given in the other two
phases. Hence, once the initial conditions are imposed, the linear scalar and
tensor perturbations will be uniquely determined. Considering two different
sets of initial conditions, one imposed during the contracting phase and the
other at the bounce, we calculate the Bogoliubov coefficients and find that the
two sets yield the same results and all lead to particle creations at the onset
of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor
power spectra become scale-dependent. Comparing with the Planck 2015 data, we
find constraints on the total e-folds that the universe must have expanded
since the bounce, in order to be consistent with current observations.
