Quantum behavior of the "Little Sibling" of the Big Rip induced by a three-form field

TL;DR

This paper performs a canonical quantization of a three-form field model in a universe approaching a Little Sibling of the Big Rip, revealing quantum states where the universe's wave function vanishes, indicating potential avoidance of the singularity.

Contribution

It introduces a Wheeler-DeWitt quantization approach for three-form fields in cosmology and analyzes the quantum behavior near the LSBR event, highlighting the importance of matter content in quantum smoothing.

Findings

Existence of quantum states with vanishing wave function at LSBR

Quantum states depend on the matter content inducing LSBR

Quantum smoothing of the LSBR event is possible

Abstract

A canonical quantization \`a la Wheeler-DeWitt is performed for a model of three-form fields in a homogeneous and isotropic universe. We start by carrying out the Hamiltonian formalism of this cosmological model. We then apply this formalism to a Little Sibling of the Big Rip (LSBR), an abrupt event milder than a Big Rip and that is known to be generic to several minimally coupled three-form fields for a variety of potentials. We obtain a set of analytical solutions of the Wheeler-DeWitt equation using different analytical approximations and explore the physical consequences of them. It turns out that there are quantum states where the wave function of the universe vanishes, i.e. the DeWitt condition is fulfilled for them. Given that this happens only for some subset of solutions of the Wheeler-DeWitt equation, this points out that the matter inducing the LSBR is equally important in the process as, it has been previously shown, a minimally coupled phantom scalar field feeding classically a LSBR is smoothed at the quantum level, i.e. all the quantum states lead to a vanishing wave function.