# The classical and quantum fate of the Little Sibling of the Big Rip in $f(R)$ cosmology

## TL;DR

This paper investigates the classical and quantum aspects of the Little Sibling of the Big Rip in $f(R)$ gravity, showing that quantum effects could potentially prevent this cosmological singularity.

## Contribution

It identifies specific $f(R)$ gravity models that reproduce the Little Sibling of the Big Rip and demonstrates that quantum geometrodynamics may avoid this event.

## Key findings

- Certain $f(R)$ models replicate the classical Little Sibling of the Big Rip.
- Quantum analysis suggests the event can be avoided in $f(R)$ quantum cosmology.
- The DeWitt criterion is satisfied, indicating potential singularity resolution.

## Abstract

The Little Sibling of the Big Rip is a cosmological abrupt event predicted by some phantom cosmological models that could describe our Universe. When this event is approached the observable Universe and its expansion rate grow infinitely, but its cosmic derivative remains finite. In this work we have obtained the group of metric $f(R)$ theories of gravity that reproduce this classical cosmological background evolution. Furthermore, we have considered the quantization of some of the resulting models in the framework of quantum geometrodynamics, showing that the DeWitt criterion can be satisfied. Therefore, as it also happens in General Relativity, this event may be avoided in $f(R)$ quantum cosmology.