Loop quantum geometry effects and the tunneling wavefunction proposal

It is generally expected that quantum gravity effects can produce a repulsive force of gravity causing a bounce which resolves the singularity. Loop quantum cosmology is one arena in which a non-singular bounce resulting from holonomy modifications has been shown to be generic feature of various spacetimes. Due to the presence of bounce, the effective minisuperspace potential in a quantum cosmology setting resulting from such models is step-like or infinite near the classical big bang. Absence of a barrier potential, as in Wheeler-DeWitt theory, suggests that the Vilenkin's tunneling wavefunction proposal is incompatible since the universe can not tunnel from nothing at the zero scale factor. We examine this issue in the case of LQC for a spatially closed FLRW model sourced with a positive cosmological constant and show that if one includes inverse volume effects as suggested by underlying quantum geometry then the step-like potential is modified to a barrier potential with height higher than that of the Wheeler-DeWitt case. Then, we realized that generally the universe can tunnel to inflationary universe or cyclic universe depending on the value of cosmological constant.