Tunneling wavefunction proposal with loop quantum geometry effects

TL;DR

This paper investigates the viability of Vilenkin's tunneling wavefunction proposal within loop quantum cosmology, demonstrating that quantum geometric effects can resolve singularities and enable tunneling to cyclic universes.

Contribution

It shows that inverse scale factor modifications in LQC restore the tunneling barrier, providing a non-singular completion of the tunneling proposal and allowing tunneling to cyclic universes.

Findings

Quantum geometry effects replace the classical barrier with a quantum one.

The universe is non-singular and static at zero scale factor.

Tunneling to a cyclic universe is possible with a large cosmological constant.

Abstract

In Vilenkin's tunneling wavefunction 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 FLRW 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 step like 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 non-singular and in an Einstein static like phase. We show that quantum geometric effects in LQC provide a non-singular 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.