Tunneling probability for the birth of universes with radiation, cosmological constant and an ad hoc potential

TL;DR

This paper investigates the quantum tunneling process that could lead to the birth of FLRW universes with radiation and a cosmological constant, highlighting the role of an ad hoc potential in enabling universe creation for different spatial curvatures.

Contribution

It introduces an ad hoc potential in quantum cosmology models, demonstrating its effect in creating a tunneling barrier for universe nucleation across various curvatures.

Findings

Ad hoc potential creates a tunneling barrier for universe birth.

Tunneling probabilities are computed for different curvature models.

Universe creation is possible via tunneling for any spatial curvature.

Abstract

In this work we study the birth of Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) models with zero ($k=0$) and negative ($k=-1$) curvatures of the spatial sections. The material content of the models is composed of a radiation perfect fluid and a positive cosmological constant. The models also have the presence of an ad hoc potential which origin is believed to be of geometrical nature. In order to describe the birth of these universes, we quantize them using quantum cosmology. Initially, we obtain the Wheeler-DeWitt equations and solve them using the WKB approximation. We notice that the presence of the ad hoc potential produces a barrier for any value of $k$. It means that we may describe the birth of the universe through a tunneling mechanism, for any curvature of the spatial sections, not only for the usual case $k=1$. We, explicitly, compute the tunneling probabilities for the birth of the different models of the universe and compare these tunneling probabilities.