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Finite-time future singularities in modified Gauss–Bonnet and ℱ(R,G) gravity and singularity avoidance

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Abstract

We study all four types of finite-time future singularities emerging in the late-time accelerating (effective quintessence/phantom) era from ℱ(R,G)-gravity, where R and G are the Ricci scalar and the Gauss–Bonnet invariant, respectively. As an explicit example of ℱ(R,G)-gravity, we also investigate modified Gauss–Bonnet gravity, so-called F(G)-gravity. In particular, we reconstruct the F(G)-gravity and ℱ(R,G)-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in F(G)-gravity and ℱ(R,G)-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss–Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory a non-singular one as well.

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Authors and Affiliations

  1. Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, 300

    Kazuharu Bamba

  2. Campus UAB, Facultat de Ciencies, Instituciò Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Ciencies de l’Espai (IEEC-CSIC), Torre C5-Par-2a pl, 08193, Bellaterra (Barcelona), Spain

    Sergei D. Odintsov

  3. Dipartimento di Fisica, Università di Trento and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Trento, Trento, Italy

    Lorenzo Sebastiani & Sergio Zerbini

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  1. Kazuharu Bamba
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  2. Sergei D. Odintsov
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  3. Lorenzo Sebastiani
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  4. Sergio Zerbini
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Correspondence to Kazuharu Bamba.

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Also at Tomsk State Pedagogical University.

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Bamba, K., Odintsov, S.D., Sebastiani, L. et al. Finite-time future singularities in modified Gauss–Bonnet and ℱ(R,G) gravity and singularity avoidance. Eur. Phys. J. C 67, 295–310 (2010). https://doi.org/10.1140/epjc/s10052-010-1292-8

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