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Abstract

Extended theories of gravity have gathered a lot of attention over the last
years, for they not only provide an excellent framework to describe the
inflationary era but also yields an alternative to the elusive and mysterious
dark energy. Among the different extended theories of gravity, on this work we
focus on metric $f(R)$ theories. In addition, it is well known that if the
late-time acceleration of the universe is stronger than the one induced by a
cosmological constant then some future cosmic singularities might arise, being
the Big Rip the most virulent one. Following this reasoning, on this work, we
analyse the Big Rip singularity in the framework of $f(R)$ quantum
geometrodynamics. Invoking the DeWitt criterium, i. e. that the wave function
vanishes at the classical singularity, we proof that a class of solutions to
the Wheeler-DeWitt equation fulfilling this condition can be found. Therefore,
this result hints towards the avoidance of the Big Rip in metric $f(R)$
theories of gravity.