Implications of quantum ambiguities in k=1 loop quantum cosmology:
  distinct quantum turnarounds and the super-Planckian regime
  The spatially closed Friedmann-Lema\^{i}tre-Robertson-Walker model in loop
quantum cosmology admits two inequivalent consistent quantizations: one based
on expressing the field strength in terms of the holonomies over closed loops,
and, another using a connection operator and open holonomies. Using the
effective dynamics, we investigate the phenomenological differences between the
two quantizations for the single fluid and the two fluid scenarios with various
equations of state, including the phantom matter. We show that a striking
difference between the two quantizations is the existence of two distinct
quantum turnarounds, either bounces or recollapses, in the connection
quantization, in contrast to a single distinct quantum bounce or a recollapse
in the holonomy quantization. These results generalize an earlier result on the
existence of two distinct quantum bounces for stiff matter by Corichi and
Karami. However, we find that in certain situations two distinct quantum
turnarounds can become virtually indistinguishable. And depending on the
initial conditions, a pure quantum cyclic universe can also exist undergoing a
quantum bounce and a quantum recollapse. We show that for various equations of
states, connection based quantization leads to super-Planckian values of the
energy density and the expansion scalar at quantum turnarounds. Interestingly,
we find that very extreme energy densities can also occur for the holonomy
quantization, breaching the maximum allowed density in the spatially flat loop
quantized model. However, the expansion scalar in all these cases is bounded by
a universal value.
