Loop Quantum Cosmology Scalar Field Models
  In this work we use the Loop Quantum Cosmology modified scalar-tensor
reconstruction techniques in order to investigate how bouncing and inflationary
cosmologies can be realized. With regard to the inflationary cosmologies, we
shall be interested in realizing the intermediate inflation and the Type IV
singular inflation, while with regard to bouncing cosmologies, we shall realize
the superbounce and the symmetric bounce. In all the cases, we shall find the
kinetic term of the LQC holonomy corrected scalar-tensor theory and the
corresponding scalar potential. In addition, we shall include a study of the
effective equation of state, emphasizing at the early and late time eras. As we
demonstrate, in some cases it is possible to have a nearly de Sitter equation
of state at the late-time era, a result that could be interpreted as the
description of a late-time acceleration era. Also, in all cases we shall
examine the dynamical stability of the LQC holonomy corrected scalar-tensor
theory, and we shall confront the results with those coming from the
corresponding classical dynamical stability theory. The most appealing
cosmological scenario is that of a Type IV singular inflationary scenario, in
which the singularity may occur at the late-time era. As we demonstrate, for
this model, during the dark energy era, a transition from non-phantom to a
phantom dark energy era occurs.
