Classical and quantum $f(R)$ cosmology: The big rip, the little rip and the little sibling of the big rip

TL;DR

This paper reviews how classical and quantum $f(R)$ gravity theories predict or potentially avoid catastrophic future singularities like the big rip, analyzing the role of quantum effects in smoothing these cosmic doomsdays.

Contribution

It provides a comprehensive analysis of classical and quantum $f(R)$ gravity models concerning future singularities, including the application of the DeWitt criterion for singularity avoidance.

Findings

Quantum effects may prevent classical singularities in $f(R)$ cosmology.

The DeWitt criterion is analyzed for singularity avoidance.

Classical and quantum predictions differ in the fate of cosmic doomsdays.

Abstract

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark energy models that could describe the future evolution of our Universe. When the universe evolves towards either of these future cosmic events all bounded structures and, ultimately, space-time itself are ripped apart. Nevertheless, it is commonly belief that quantum gravity effects may smooth or even avoid these classically predicted singularities. In this review, we discuss the classical and quantum occurrence of these riplike events in the scheme of metric $f(R)$ theories of gravity. The quantum analysis is performed in the framework of $f(R)$ quantum geometrodynamics. In this context, we analyse the fulfilment of the DeWitt criterion for the avoidance of these singular fates.