Qualitative dynamics and inflationary attractors in loop cosmology
  Qualitative dynamics of three different loop quantizations of spatially flat
isotropic and homogeneous models is studied using effective spacetime
description of the underlying quantum geometry. These include the standard loop
quantum cosmology (LQC), its recently revived modification (referred to as
mLQC-I), and another related modification of LQC (mLQC-II) whose dynamics is
studied in detail for the first time. Various features of LQC, including
quantum bounce and pre-inflationary dynamics, are found to be shared with the
mLQC-I and mLQC-II models. We study universal properties of dynamics for
chaotic inflation, fractional monodromy inflation, Starobinsky potential,
non-minimal Higgs inflation, and an exponential potential. We find various
critical points and study their stability, which reveal various qualitative
similarities in the post-bounce phase for all these models. The pre-bounce
qualitative dynamics of LQC and mLQC-II turns out to be very similar, but is
strikingly different from that of mLQC-I. In the dynamical analysis, some of
the fixed points turn out to be degenerate for which center manifold theory is
used. For all these potentials, non-perturbative quantum gravitational effects
always result in a non-singular inflationary scenario with a phase of
super-inflation succeeded by the conventional inflation. We show the existence
of inflationary attractors, and obtain scaling solutions in the case of the
exponential potential. Since all of the models agree with general relativity at
late times, our results are also of use in classical theory where qualitative
dynamics of some of the potentials has not been studied earlier.
