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

TL;DR

This paper investigates whether quantum effects in metric $f(R)$ gravity can prevent the Big Rip singularity, showing that certain quantum solutions vanish at the classical singularity, suggesting singularity avoidance.

Contribution

It demonstrates that solutions to the Wheeler-DeWitt equation in $f(R)$ quantum cosmology can satisfy the DeWitt criterion, indicating potential avoidance of the Big Rip singularity.

Findings

Wave function solutions vanish at the classical singularity

Quantum $f(R)$ gravity may prevent the Big Rip

Supports the idea of singularity avoidance in quantum cosmology

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.