Finite time pseudo-rip singularity in cosmology

By studying first a new decelerating sudden future singularity (SFS) universe we report finding a novel type of cosmological singularity which we dub a finite time pseudo-rip (FTPR) because unlike for a pseudo-rip, it happens in the finite future of the universe. In contrast to the new SFS model, where the expansion is decelerating before reaching the pressure singularity, the FTPR scenario is preceded by a super-accelerated phantom phase. Our claim is based on the thorough study of the energy conditions showing the violations of all of them for a FTPR, and only the dominant energy one for an SFS. Application of the so-called Raychaudhuri averaging shows that, alike within the requirement of geodesic completeness, these singularities are weak in the sense of this definition. We study the properties of the models including the behaviour of the cosmological horizons presented in the appropriate Penrose diagrams. Finally, we introduce a FTPR model containing standard radiation and dust fluids that can mimic the past expansion history of $\Lambda$CDM though facing a future pressure singularity.