$f(R)$ quantum cosmology: avoiding the Big Rip

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.