Quantum Cosmology of the Big Rip: Within GR and in a Modified Theory of Gravity

Quantum gravity is the theory that is expected to successfully describe systems that are under strong gravitational effects while at the same time being of an extreme quantum nature. When this principle is applied to the universe as a whole, we use what is commonly named “quantum cosmology”. So far we do not have a definite quantum theory of gravity or cosmology, but we have several promising approaches. Here we will review the application of the Wheeler–DeWitt formalism to the late-time universe, where it might face a Big Rip future singularity. The Big Rip singularity is the most virulent future dark energy singularity which can happen not only in general relativity but also in some modified theories of gravity. Our goal in this paper is to review two simple setups of the quantisation of the Big Rip in a Friedmann–Lemaître–Robertson–Walker universe within general relativity and in a modified theory of gravity.