  It is generally expected that in a non-singular cosmological model a cyclic
evolution is straightforward to obtain on introduction of a suitable choice of
a scalar field with a negative potential or a negative cosmological constant
which causes a recollapse at some time in the evolution. We present a counter
example to this conventional wisdom. Working in the realm of loop cosmological
models with non-perturbative quantum gravity modifications we show that a
modified version of standard loop quantum cosmology based on Thiemann's
regularization of the Hamiltonian constraint while generically non-singular
does not allow a cyclic evolution unless some highly restrictive conditions
hold. Irrespective of the energy density of other matter fields, a recollapse
and hence a cyclic evolution is only possible if one chooses an almost Planck
sized negative potential of the scalar field or a negative cosmological
constant. Further, cycles when present do not occur in the classical regime.
Surprisingly, a necessary condition for a cyclic evolution, not singularity
resolution, turns out to be a violation of the weak energy condition. These
results are in a striking contrast to standard loop quantum cosmology where
obtaining a recollapse at large volumes and a cyclic evolution is
straightforward, and, there is no violation of weak energy condition. On one
hand our work shows that some quantum cosmological models even though
non-singular and bouncing are incompatible with a cyclic evolution, and on the
other hand demonstrates that differences in various quantization prescriptions
in loop cosmology need not be faint and buried in the pre-bounce regime, but
can be striking and profound even in the post-bounce regime.
