  It was recently shown that tunneling wavefunction proposal is consistent with
loop quantum geometry corrections including both holonomy and inverse scale
factor corrections in the gravitational part of a spatially closed isotropic
model with a positive cosmological constant. However, in presence of an
inflationary potential the initial singularity is kinetic dominated and the
effective minisuperspace potential again diverges at zero scale factor. Since
the wavefunction in loop quantum cosmology cannot increase towards the zero
scale factor, the tunneling wavefunction seems incompatible. We show that
consistently including inverse scale factor modifications in scalar field
Hamiltonian changes the effective potential into a barrier potential allowing
the tunneling proposal. We also discuss a potential quantum instability of the
cyclic universe resulting from tunneling.
