Quantum Tunneling Effect in Oscillating Friedmann Cosmology

TL;DR

This paper explores quantum tunneling in oscillating Friedmann cosmology, revealing that tunneling can occur at maximum expansion, leading to universe recollapse or oscillations, with probabilities depending on matter content and cosmological constant.

Contribution

It demonstrates that quantum tunneling in cosmology can occur not only at universe boundaries but also at maximum expansion, introducing new insights into universe evolution scenarios.

Findings

Tunneling occurs at maximum expansion in Friedmann universe.

Probability of tunneling depends on matter content and cosmological constant.

Oscillating universe can tunnel to recollapse, with explicit probability formula.

Abstract

It is shown that the tunneling effect in quantum cosmology is possible not only at the very beginning or the very end of the evolution, but also at the moment of maximum expansion of the universe. A positive curvature expanding Friedmann universe changes its state of evolution spontaneously and completely, {\it without} any changes in the matter content, avoiding recollapse, and falling into oscillations between the nonzero values of the scale factor. On the other hand, an oscillating nonsingular universe can tunnel spontaneously to a recollapsing regime. The probability of such kind of tunneling is given explicitly. It is inversely related to the amount of nonrelativistic matter (dust), and grows from a certain fixed value to unity if the negative cosmological constant approaches zero.