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Cosmic acceleration in non-flat f(T) cosmology

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Abstract

We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-\(\sigma \) confidence level, emphasizing the fact that \(\Omega _{k0}\) turns out to be non-compatible with zero at least at 1\(\sigma \). Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the \(\Lambda \)CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the \(\Lambda \)CDM predictions.

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Notes

  1. The presence of matter and dark energy manifests a redshift at which dark energy starts dominating over matter, i.e. the transition redshift \(z_{tr}\).

  2. In the framework of metric formalism.

  3. For the sake of clearness, to avoid the a priori chosen cosmological model, one can calibrate on a model-independent local regression estimate of \(\mu (z)\) using Union supernova sample. This leads to a GRB Hubble diagram made out of 69 GRBs [42].

  4. Hereafter, Latin indexes refer to as the tangent space, whereas Greek indexes label as manifold coordinates.

  5. It is commonly accepted that viable alternatives to the cosmological constant \(\Lambda \) provide as a limiting case at \(z\simeq 0\), the concordance paradigm. In other words, it seems that the best models capable of describing the universe dynamics today are those which reduce to a constant dark energy term at small redshift domains.

  6. This case is excluded by recent observations.

  7. We assume T and \(T_0\) negative and p positive definite.

  8. The meaning of arbitrary new “redshift” variables has been introduced to overcome the convergence problem. It deals with the fact that most of cosmic data lie on redshift domains \(z\ge 1\), while Taylor expansions are built up at \(z\simeq 0\). Introducing \(y_i\) would statistically favors the cosmographic analyses, instead of using z only.

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Acknowledgements

The work is partly supported by VEGA Grant No. 2/0009/16 and from COST Action CA15117 ”Cosmology and Astrophysics Network for Theoretical Advances and Training Actions” (CANTATA), supported by COST (European Cooperation in Science and Technology). S. Capozziello and O. Luongo are supported by Istituto Nazionale di Fisica Nucleare (INFN). R. Pincak would like to thank the TH division at CERN for hospitality.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Napoli “Federico II”, Via Cinthia, 80126, Naples, Italy

    Salvatore Capozziello

  2. Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia 9, 80126, Naples, Italy

    Salvatore Capozziello

  3. Gran Sasso Science Institute, Via F. Crispi 7, 67100, L’Aquila, Italy

    Salvatore Capozziello

  4. Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044, Frascati, Italy

    Orlando Luongo

  5. School of Science and Technology, University of Camerino, 62032, Camerino, Italy

    Orlando Luongo

  6. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, AP 70543, Mexico, DF, 04510, Mexico

    Orlando Luongo

  7. Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 043 53, Kosice, Slovakia

    Richard Pincak

  8. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia, 141980

    Richard Pincak

  9. Department of Physics, Vali-e-Asr University, Rafsanjan, Iran

    Arvin Ravanpak

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  1. Salvatore Capozziello
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  2. Orlando Luongo
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  3. Richard Pincak
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  4. Arvin Ravanpak
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Correspondence to Orlando Luongo.

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Capozziello, S., Luongo, O., Pincak, R. et al. Cosmic acceleration in non-flat f(T) cosmology. Gen Relativ Gravit 50, 53 (2018). https://doi.org/10.1007/s10714-018-2374-4

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