  Loop quantum cosmology is a symmetry reduced quantization of cosmological
spacetimes based on loop quantum gravity. While it has been successful in
resolution of various cosmological singularities and connecting Planck scale
physics to phenomenology, its connection with loop quantum gravity has remained
elusive. It is therefore important to integrate more and more features of the
full theory into this framework and understand the reliability of physical
predictions. In particular, if one wishes to connect the effective Hamiltonian
in loop quantum cosmology to an expectation value of the scalar constraint
operator in suitable coherent states for the full theory, one has to go beyond
the standard setting of loop quantum cosmology. One possibility is to introduce
gauge-covariant fluxes, which become necessary because the presence of a finite
regularization parameter causes functions build out of the standard discretized
variables to be in general not gauge invariant. Following the construction of
gauge-covariant fluxes pioneered by Thiemann in [1], we show that the physics
of loop quantum cosmology is affected in a non-trivial way. The bounce turns
out to be generically asymmetric with a rescaling of the Newton's constant in
the pre-bounce branch. Gauge-covariant fluxes result in a higher order quantum
difference equation in comparison to loop quantum cosmology. Even the behavior
of matter, which behaves innocuously in loop quantum cosmology, is enriched,
resulting in an effective non-minimal coupling. These effects are shown to be
common to different choices of regularization parameters.
