f(R) quantum cosmology: Avoiding the big rip

Extended theories of gravity have gathered a lot of attention over the past years, for they not only provide an excellent framework to describe the inflationary era but also yield an alternative to the elusive and mysterious dark energy. Among the different extended theories of gravity, in 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, the big rip being the most virulent one. Following this reasoning, in this work, we analyze the big rip singularity in the framework of f(R) quantum geometrodynamics. Invoking the DeWitt criterion, i.e., that the wave function vanishes at the classical singularity, we prove that a class of solutions to the Wheeler-DeWitt equation fulfilling this condition can be found. Therefore, this result hints toward the avoidance of the big rip in metric f(R) theories of gravity.