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Tradeoff between smoother and sooner “little rip”

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Abstract

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.

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Notes

  1. For an alternative classifications of dark energy related singularities, see the Refs. [14] and [15].

  2. We leave the induced gravity parameter γ arbitrary and do not set it to unity as was done in Ref. [53].

  3. Notice that we have excluded the limiting case where μ 2=1/4α corresponding to the Chern–Simons gravity, because in that case a homogeneous and isotropic brane cannot be embedded in the bulk [54].

  4. Phantom energy does not always imply future singularities as was shown, for example, in Ref. [40].

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Acknowledgements

M.B.L. is supported by the Basque Foundation for Science IKERBASQUE. She also wishes to acknowledge the hospitality of LeCosPA Center at the National Taiwan University during the completion of part of this work and the support of the Portuguese Agency “Fundação para a Ciência e Tecnologia” through PTDC/FIS/111032/2009. P.C. and Y.W.L. are supported by Taiwan National Science Council under Project No. NSC 97-2112-M-002-026-MY3 and by Taiwan’s National Center for Theoretical Sciences (NCTS). P.C. is in addition supported by US Department of Energy under Contract No. DE-AC03-76SF00515. This work has been supported by a Spanish-Taiwanese Interchange Program with reference 2011TW0010 (Spain) and NSC 101-2923-M-002-006-MY3 (Taiwan).

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Authors and Affiliations

  1. Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080, Bilbao, Spain

    Mariam Bouhmadi-López

  2. IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain

    Mariam Bouhmadi-López

  3. Department of Physics, National Taiwan University, Taipei, 10617, Taiwan

    Pisin Chen & Yen-Wei Liu

  4. Graduate Institute of Astrophysics, National Taiwan University, Taipei, 10617, Taiwan

    Pisin Chen

  5. Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan

    Pisin Chen & Yen-Wei Liu

  6. Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94305, USA

    Pisin Chen

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  1. Mariam Bouhmadi-López
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Correspondence to Mariam Bouhmadi-López.

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Bouhmadi-López, M., Chen, P. & Liu, YW. Tradeoff between smoother and sooner “little rip”. Eur. Phys. J. C 73, 2546 (2013). https://doi.org/10.1140/epjc/s10052-013-2546-z

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