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

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Abstract

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.

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Notes

  1. It has also been examined in Stefancic (2005) that for α<0, when ρ→0, there can appear the Type II singularity.

  2. For clarity, we use the notation “F(R)” gravity and “f(T)” gravity throughout this review.

  3. In this section, the metric signature of (+,−,−,−) is adopted.

  4. Note that such a model does not pass the matter instability test and therefore some viable generalizations (Nojiri and Odintsov 2007c, 2008c; Cognola et al. 2008; Bamba et al. 2012b) have been proposed.

  5. Note that the correct expressions for (ϕ 0,ϕ 2,ϕ 3) may still formally be written as Eqs. (648)–(651), but the polynomials entering them are now different and also depend on powers of ε.

  6. Note that, in Kim et al. (2004), the authors assume the data are separated in redshift bins so that the error becomes \(\sigma^{2} = \sigma_{sys}^{2}/{\mathcal{N}}_{bin} + {\mathcal{N}}_{bin} (z/z_{max})^{2} \sigma_{m}^{2}\) with \({\mathcal{N}}_{bin}\) the number of SNeIa in a bin. However, we prefer to not bin the data so that \({\mathcal{N}}_{bin} = 1\).

  7. Actually, such estimates have been obtained by computing the mean and the standard deviation from the marginalized likelihoods of the cosmographic parameters. Hence, the central values do not represent exactly the best fit model, while the standard deviations do not give a rigorous description of the error because the marginalized likelihoods are manifestly non-Gaussian. Nevertheless, we are mainly interested in an order of magnitude estimate so that we would not care about such statistical details.

References