Tunneling wave function proposal with loop quantum geometry effects

Abstract

In Vilenkin's tunneling wave function proposal our expanding Universe is born via a tunneling through a barrier from nothing at the zero scale factor. We explore the viability of this proposal for the spatially-closed Friedmann-Lema\^{\i}tre-Robertson-Walker model with a positive cosmological constant including quantum gravity modifications in the Planck regime. Our setting is the effective spacetime description of loop quantum cosmology (LQC) which is known to replace the big bang singularity with a bounce due to the holonomy modifications. Due to the bounce, the barrier potential of the Wheeler-DeWitt theory is replaced by a steplike potential which makes the tunneling proposal incompatible. But for a complete picture of singularity resolution, inverse scale-factor modifications from quantum geometry must be included which play an important role at very small scale factors in the spatially closed models. We show that with inclusion of inverse scale-factor modifications the resulting potential is again a barrier potential. The Universe at the vanishing scale factor is dynamically nonsingular and in an Einstein staticlike phase. We show that quantum geometric effects in LQC provide a nonsingular completion of Vilenkin's tunneling proposal. We also find that quantum geometric effects result in a possibility of a tunneling to a quantum cyclic universe albeit for a very large value of cosmological constant determined by the quantum geometry.