Tradeoff between smoother and sooner “little rip”

There exist dark-energy models that predict the occurrence of a “little rip”. At the point of a little rip the Hubble rate and its cosmic time derivative approach infinity, which is quite similar to the big rip singularity except that the former happens at infinite future and the latter at a finite cosmic time; both events happen in the future and at high energies. In the case of the big rip, a combination of ultra-violet and infra-red effects can smooth its doomsday. We therefore wonder if the little rip can also be smoothed in a similar way. We address the ultra-violet and infra-red effects in general relativity through a brane-world model with a Gauss–Bonnet term in the bulk and an induced gravity term on the brane. We find that the little rip is transformed in this case into a sudden singularity, or a “big brake”. Even though the big brake is smoother than the little rip in that the Hubble rate is finite at the event, the trade-off is that it takes place sooner, at a finite cosmic time. In our estimate, the big brake would happen at roughly 1300 Gyr