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The big rip, the little rip and the little sibling of the big rip arecosmological doomsdays predicted by some phantom dark energy models that coulddescribe the future evolution of our Universe. When the universe evolvestowards either of these future cosmic events all bounded structures and,ultimately, space-time itself are ripped apart. Nevertheless, it is commonlybelief that quantum gravity effects may smooth or even avoid these classicallypredicted singularities. In this review, we discuss the classical and quantumoccurrence of these riplike events in the scheme of metric $f(R)$ theories ofgravity. The quantum analysis is performed in the framework of $f(R)$ quantumgeometrodynamics. In this context, we analyse the fulfilment of the DeWittcriterion for the avoidance of these singular fates.

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