Reconstructing the Universe Evolution from Loop Quantum Cosmology Scalar
  Fields
  We extend the scalar-tensor reconstruction techniques for classical cosmology
frameworks, in the context of loop quantum cosmology. After presenting in some
detail how the equations are generalized in the loop quantum cosmology case, we
discuss which new features and limitations does the quantum framework brings
along, and we use various illustrative examples in order to demonstrate how the
method works. As we show the energy density has two different classes of
solutions, and one of these yields the correct classical limit while the second
captures the quantum phenomena. We study in detail the scalar tensor
reconstruction method for both these solutions. Also we discuss some scenarios
for which the Hubble rate becomes unbounded at finite time, which corresponds
for example in a case that a Big Rip occurs. As we show this issue is
non-trivial and we discuss how this case should be treated in a consistent way.
Finally, we investigate how the classical stability conditions for the
scalar-tensor solutions are generalized in the loop quantum framework.
