Oscillating universe in massive gravity

TL;DR

This paper explores cosmic evolutions in ghost-free massive gravity, revealing oscillating and bouncing universes that can resolve the big bang singularity, and analyzing the stability of Einstein static states.

Contribution

It introduces a method to analyze cosmic evolution in massive gravity and demonstrates the existence of oscillating, bouncing, and stable static solutions with implications for singularity resolution.

Findings

Existence of oscillating and bouncing universe solutions.

Stable Einstein static universe states are possible but not eternally stable.

Quantum tunneling can lead the universe from oscillating to expanding phases.

Abstract

Massive gravity is a modified theory of general relativity. In this paper, we study, using a method in which the scale factor changes as a particle in a "potential", all possible cosmic evolutions in a ghost-free massive gravity. We find that there exists, in certain circumstances, an oscillating universe or a bouncing one. If the universe starts at the oscillating region, it may undergo a number of oscillations before it quantum mechanically tunnels to the bounce point and then expand forever. But going back to the singularity from the oscillating region is physically not allowed. So, the big bang singularity can be successfully resolved. At the same time, we also find that there exists a stable Einstein static state in some cases. However, the universe can not stay at this stable state past-eternally since it is allowed to quantum mechanically tunnel to a big-bang-to-big-crunch region and end with a big crunch. Thus, a stable Einstein static state universe can not be used to avoid the big bang singularity in massive gravity.