The little rip in classical and quantum $f(R)$ cosmology

TL;DR

This paper investigates the little rip cosmological event within classical and quantum $f(R)$ gravity frameworks, showing that quantum effects may prevent the occurrence of the little rip, similar to results in general relativity.

Contribution

It provides the first analysis of the little rip in $f(R)$ quantum cosmology using the Wheeler-DeWitt equation, demonstrating potential avoidance of the event.

Findings

Quantum analysis satisfies the DeWitt criterion.

Quantum effects may prevent the little rip in $f(R)$ cosmology.

Results align with classical general relativity predictions.

Abstract

The little rip is a cosmological abrupt event predicted by some phantom dark energy models that could describe the future evolution of our Universe. This event can be interpreted as a big rip singularity delayed indefinitely, although in those models bounded structures will be destroyed in a finite cosmic time in the future. In this work, we analyse the little rip cosmology from a classical and quantum point of view within the scheme of alternative metric $f(R)$ theories of gravity. The quantum analysis is performed in the framework of $f(R)$ quantum geometrodynamics by means of the modified Wheeler-DeWitt equation. In this context, we show that the DeWitt criterion can be satisfied. Similar to what happens in general relativity, this result points towards the avoidance of the little rip in $f(R)$ quantum cosmology.