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Finite time pseudo-rip singularity in cosmology

Mariusz P. Dąbrowski, Teodor Borislavov Vasilev

TL;DR

The paper tackles the problem of classifying future cosmological singularities beyond the big rip by constructing two explicit FLRW models through targeted Hubble-rate prescriptions: a decelerating sudden future singularity (SFS) and a finite-time pseudo-rip (FTPR). It analyzes their energy-condition violations, horizon structure via Penrose diagrams, and the strength of the singularities using Raychaudhuri spacetime averaging. The decelerating SFS exhibits a Type II pressure singularity with NEC preserved and DEC violated near the singularity, while the FTPR features phantom-dominated dynamics with violations of all energy conditions, yet both are weak in the Raychaudhuri sense and geodesically extendible. Together, these results clarify distinctions between SFS and FTPR and provide a practical framework for exploring exotic singularities and potential cyclic cosmologies within General Relativity.

Abstract

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.

Finite time pseudo-rip singularity in cosmology

TL;DR

The paper tackles the problem of classifying future cosmological singularities beyond the big rip by constructing two explicit FLRW models through targeted Hubble-rate prescriptions: a decelerating sudden future singularity (SFS) and a finite-time pseudo-rip (FTPR). It analyzes their energy-condition violations, horizon structure via Penrose diagrams, and the strength of the singularities using Raychaudhuri spacetime averaging. The decelerating SFS exhibits a Type II pressure singularity with NEC preserved and DEC violated near the singularity, while the FTPR features phantom-dominated dynamics with violations of all energy conditions, yet both are weak in the Raychaudhuri sense and geodesically extendible. Together, these results clarify distinctions between SFS and FTPR and provide a practical framework for exploring exotic singularities and potential cyclic cosmologies within General Relativity.

Abstract

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.
Paper Structure (10 sections, 38 equations, 4 figures, 1 table)

This paper contains 10 sections, 38 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. New exotic singularity models
  3. A decelerating sudden future singularity model
  4. An accelerating towards a pseudo-rip singularity model
  5. Energy conditions for new models
  6. Decelerating SFS model
  7. Accelerating PR model
  8. Singularities and horizons
  9. Raychaudhuri averaging and related strength of exotic singularities
  10. Conclusion

Figures (4)

  • Figure 1: The evolution of the decelerating model (\ref{['eq:model']}) for $n=0.2$. Left panel: the late-time evolution of the pressure $p$ given by (\ref{['eq:EoS']}). Right panel: the evolution of the equation of state parameter $w$ according to (\ref{['eq:EoS']}).
  • Figure 2: The evolution of the decelerating scale factor (\ref{['scalefactor']}) in time, normalized by the appropriate values at SFS (here $n=0.2$).
  • Figure 3: The evolution of the accelerating model (\ref{['eq:model2']}) for $n=0.2$ and $H_1a_s^{-2}=H_2a_s^{n}=1$. Left panel: late time evolution of the acceleration $\ddot{a}/a$. Right panel: the evolution of the equation of state parameter $w$.
  • Figure 4: Comparison of the Penrose diagrams for the models discussed in this section, where EH stands for the event horizon, PH for the particle horizon, and AH is the apparent horizon. Left panel: diagram for the model (\ref{['eq:model']}) representing a decelerating SFS with $n=0.2$. Right panel: diagram for the accelerating model (\ref{['eq:model2']}) with $n=0.2$, $a_s=1$ and $H_1=H_2=1$. In addition, $r_{AH}^\star$ represents the spatial radius of AH evaluated at the FTPR.