Astrophysics and Space Science

, Volume 342, Issue 1, pp 155–228

Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

  • Kazuharu Bamba
  • Salvatore Capozziello
  • Shin’ichi Nojiri
  • Sergei D. Odintsov
Invited Review


We review different dark energy cosmologies. In particular, we present the ΛCDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the ΛCDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the ΛCDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes F(R) gravity as well as F(R) Hořava-Lifshitz gravity and the teleparallel f(T) gravity. The cosmology of such models representing the ΛCDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.


Modified theories of gravity Dark energy Cosmology 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Kazuharu Bamba
    • 1
  • Salvatore Capozziello
    • 2
    • 3
  • Shin’ichi Nojiri
    • 1
    • 4
  • Sergei D. Odintsov
    • 5
    • 6
    • 7
    • 8
  1. 1.Kobayashi-Maskawa Institute for the Origin of Particles and the UniverseNagoya UniversityNagoyaJapan
  2. 2.Dipartimento di Scienze FisicheUniversità di Napoli “Federico II”NapoliItaly
  3. 3.INFN Sez. di NapoliCompl. Univ. di Monte S. AngeloNapoliItaly
  4. 4.Department of PhysicsNagoya UniversityNagoyaJapan
  5. 5.Instituciò Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain
  6. 6.Instituto de Ciencias del Espacio (CSIC) and Institut d Estudis Espacials de Catalunya (IEEC-CSIC)Facultat de CienciesBellaterra (Barcelona)Spain
  7. 7.Tomsk State Pedagogical UniversityTomskRussia
  8. 8.Eurasian International Center for Theoretical Physics and Department of General & Theoretical PhysicsEurasian National UniversityAstanaKazakhstan

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