The European Physical Journal C

, Volume 67, Issue 1–2, pp 295–310 | Cite as

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

  • Kazuharu Bamba
  • Sergei D. Odintsov
  • Lorenzo Sebastiani
  • Sergio Zerbini
Regular Article - Theoretical Physics

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.

Keywords

Dark Energy Gravity Model Dark Energy Model Future Singularity Bonnet Gravity 

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2010

Authors and Affiliations

  • Kazuharu Bamba
    • 1
  • Sergei D. Odintsov
    • 2
  • Lorenzo Sebastiani
    • 3
  • Sergio Zerbini
    • 3
  1. 1.Department of PhysicsNational Tsing Hua UniversityHsinchuTaiwan
  2. 2.Campus UAB, Facultat de CienciesInstituciò Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Ciencies de l’Espai (IEEC-CSIC)Bellaterra (Barcelona)Spain
  3. 3.Dipartimento di FisicaUniversità di Trento and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di TrentoTrentoItaly

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