Viable Inflationary Evolution from Loop Quantum Cosmology Scalar-Tensor
  Theory
  In this work we construct a bottom-up reconstruction technique for Loop
Quantum Cosmology scalar-tensor theories, from the observational indices.
Particularly, the reconstruction technique is based on fixing the functional
form of the scalar-to-tensor ratio as a function of the $e$-foldings number.
The aim of the technique is to realize viable inflationary scenarios, and the
only assumption that must hold true in order for the reconstruction technique
to work is that the dynamical evolution of the scalar field obeys the slow-roll
conditions. We shall use two functional forms for the scalar-to-tensor ratio,
one of which corresponds to a popular inflationary class of models, the
$\alpha$-attractors. For the latter, we shall calculate the leading order
behavior of the spectral index and we shall demonstrate that the resulting
inflationary theory is viable and compatible with the latest Planck and
BICEP2/Keck-Array data. In addition, we shall find the classical limit of the
theory, and as we demonstrate, the Loop Quantum Cosmology corrected theory and
the classical theory are identical at leading order in the perturbative
expansion quantified by the parameter $\rho_c$, which is the critical density
of the quantum theory. Finally, by using the formalism of slow-roll
scalar-tensor Loop Quantum Cosmology, we shall investigate how several
inflationary potentials can be realized by the quantum theory, and we shall
calculate directly the slow-roll indices and the corresponding observational
indices. In addition, the $f(R)$ gravity frame picture is presented.
