The quantum realm of the "Little Sibling" of the Big Rip singularity

TL;DR

This paper investigates the quantum behavior of the Little Sibling of the Big Rip singularity using Wheeler-DeWitt quantum cosmology, suggesting that quantum effects could potentially avoid or smooth out this cosmological singularity.

Contribution

It applies Wheeler-DeWitt quantization to the LSBR model with different degrees of freedom and approximations, exploring singularity avoidance criteria in quantum cosmology.

Findings

DeWitt condition is satisfied in all cases analyzed.

Quantum effects may prevent or smooth the LSBR singularity.

Different quantization approaches yield consistent indications of singularity avoidance.

Abstract

We analyse the quantum behaviour of the "Little Sibling" of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler--DeWitt (WDW) equation. The classical model is based on a Friedmann--Lema\^{i}tre--Robertson--Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve the WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace--Beltrami factor-ordering, using a Born--Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.