### Abstract

Both dark energy models and modified gravity theories could lead to cosmological evolutions different from either the recollapse into a Big Crunch or exponential de Sitter expansion. The newly arising singularities may represent true endpoints of the evolution or alternatively they can allow for the extension of geodesics through them. In the latter case only the components of the Riemann tensor representing tidal forces diverge. A subclass of these soft singularities, the Sudden Future Singularity (SFS) occurs at finite time, finite scale factor and finite Hubble parameter, only the deceleration parameter being divergent. In a Friedmann universe evolving in the framework of general relativity they are realized by perfect fluids with regular energy density and diverging pressure at the SFS. A particular SFS, the Big Brake occurs when the energy density vanishes and the expansion arrives at a full stop at the singularity. Such scenarios are generated by either a particular scalar field (the tachyon field) or the anti-Chaplygin gas. By adding any matter (in particular the simplest, the dust) to these models, an unwanted feature appears: at the finite scale factor of the SFS the matter energy density remains finite, implying (for a spatially flat universe) a finite Hubble parameter, hence finite expansion rate, rather then full stop. The universe would then further expand through the singularity, this nevertheless seems forbidden as the energy density of the tachyonic field / anti-Chaplygin gas would become ill-defined. This paradox is relieved in the case of the anti-Chaplygin gas by redefining its energy density and pressure in terms of distributions peaked on the singularity. The regular cosmological quantities which are continuous across the SFS are then the energy density and the square of the Hubble parameter; those allowing for a jump at the SFS are the Hubble parameter and expansion rate (both being mirror-symmetric). The pressure and the decelaration parameter will contain Dirac delta-function contributions peaked on the SFS, however this is no disadvantage as they anyhow diverge at the singularity.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Pages | 132-135 |

Number of pages | 4 |

Volume | 1514 |

DOIs | |

Publication status | Published - 2013 |

Event | Conference on Multiverse and Fundamental Cosmology, Multicosmofun 2012 - Szczecin, Poland Duration: Sep 10 2012 → Sep 14 2012 |

### Other

Other | Conference on Multiverse and Fundamental Cosmology, Multicosmofun 2012 |
---|---|

Country | Poland |

City | Szczecin |

Period | 9/10/12 → 9/14/12 |

### Fingerprint

### Keywords

- anti-Chaplygin gas
- cosmology
- soft singularities

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1514, pp. 132-135) https://doi.org/10.1063/1.4791740

**Distributional cosmological quantities solve the paradox of soft singularity crossing.** / Gergely, L.; Keresztes, Z.; Kamenshchik, Alexander Yu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIP Conference Proceedings.*vol. 1514, pp. 132-135, Conference on Multiverse and Fundamental Cosmology, Multicosmofun 2012, Szczecin, Poland, 9/10/12. https://doi.org/10.1063/1.4791740

}

TY - GEN

T1 - Distributional cosmological quantities solve the paradox of soft singularity crossing

AU - Gergely, L.

AU - Keresztes, Z.

AU - Kamenshchik, Alexander Yu

PY - 2013

Y1 - 2013

N2 - Both dark energy models and modified gravity theories could lead to cosmological evolutions different from either the recollapse into a Big Crunch or exponential de Sitter expansion. The newly arising singularities may represent true endpoints of the evolution or alternatively they can allow for the extension of geodesics through them. In the latter case only the components of the Riemann tensor representing tidal forces diverge. A subclass of these soft singularities, the Sudden Future Singularity (SFS) occurs at finite time, finite scale factor and finite Hubble parameter, only the deceleration parameter being divergent. In a Friedmann universe evolving in the framework of general relativity they are realized by perfect fluids with regular energy density and diverging pressure at the SFS. A particular SFS, the Big Brake occurs when the energy density vanishes and the expansion arrives at a full stop at the singularity. Such scenarios are generated by either a particular scalar field (the tachyon field) or the anti-Chaplygin gas. By adding any matter (in particular the simplest, the dust) to these models, an unwanted feature appears: at the finite scale factor of the SFS the matter energy density remains finite, implying (for a spatially flat universe) a finite Hubble parameter, hence finite expansion rate, rather then full stop. The universe would then further expand through the singularity, this nevertheless seems forbidden as the energy density of the tachyonic field / anti-Chaplygin gas would become ill-defined. This paradox is relieved in the case of the anti-Chaplygin gas by redefining its energy density and pressure in terms of distributions peaked on the singularity. The regular cosmological quantities which are continuous across the SFS are then the energy density and the square of the Hubble parameter; those allowing for a jump at the SFS are the Hubble parameter and expansion rate (both being mirror-symmetric). The pressure and the decelaration parameter will contain Dirac delta-function contributions peaked on the SFS, however this is no disadvantage as they anyhow diverge at the singularity.

AB - Both dark energy models and modified gravity theories could lead to cosmological evolutions different from either the recollapse into a Big Crunch or exponential de Sitter expansion. The newly arising singularities may represent true endpoints of the evolution or alternatively they can allow for the extension of geodesics through them. In the latter case only the components of the Riemann tensor representing tidal forces diverge. A subclass of these soft singularities, the Sudden Future Singularity (SFS) occurs at finite time, finite scale factor and finite Hubble parameter, only the deceleration parameter being divergent. In a Friedmann universe evolving in the framework of general relativity they are realized by perfect fluids with regular energy density and diverging pressure at the SFS. A particular SFS, the Big Brake occurs when the energy density vanishes and the expansion arrives at a full stop at the singularity. Such scenarios are generated by either a particular scalar field (the tachyon field) or the anti-Chaplygin gas. By adding any matter (in particular the simplest, the dust) to these models, an unwanted feature appears: at the finite scale factor of the SFS the matter energy density remains finite, implying (for a spatially flat universe) a finite Hubble parameter, hence finite expansion rate, rather then full stop. The universe would then further expand through the singularity, this nevertheless seems forbidden as the energy density of the tachyonic field / anti-Chaplygin gas would become ill-defined. This paradox is relieved in the case of the anti-Chaplygin gas by redefining its energy density and pressure in terms of distributions peaked on the singularity. The regular cosmological quantities which are continuous across the SFS are then the energy density and the square of the Hubble parameter; those allowing for a jump at the SFS are the Hubble parameter and expansion rate (both being mirror-symmetric). The pressure and the decelaration parameter will contain Dirac delta-function contributions peaked on the SFS, however this is no disadvantage as they anyhow diverge at the singularity.

KW - anti-Chaplygin gas

KW - cosmology

KW - soft singularities

UR - http://www.scopus.com/inward/record.url?scp=84891468858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891468858&partnerID=8YFLogxK

U2 - 10.1063/1.4791740

DO - 10.1063/1.4791740

M3 - Conference contribution

AN - SCOPUS:84891468858

SN - 9780735411357

VL - 1514

SP - 132

EP - 135

BT - AIP Conference Proceedings

ER -