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Geodesic Deviation Equation in ΛCDM \(f(T,\mathcal {T})\) Gravity

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Abstract

The geodesic deviation equation has been investigated in the framework of \(f(T,\mathcal {T})\) gravity, where T denotes the torsion and \(\mathcal {T}\) is the trace of the energy-momentum tensor, respectively. The FRW metric is assumed and the geodesic deviation equation has been established following the General Relativity approach in the first hand and secondly, by a direct method using the modified Friedmann equations. Via fundamental observers and null vector fields with FRW background, we have generalized the Raychaudhuri equation and the Mattig relation in \(f(T,\mathcal {T})\) gravity. Furthermore, we have numerically solved the geodesic deviation equation for null vector fields by considering a particular form of \(f(T,\mathcal {T})\) which induces interesting results susceptible to be tested with observational data.

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Acknowledgments

The authors thank IMSP for hospitality during the elaboration of this work.

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Authors and Affiliations

  1. Institut de Mathématiques et de Sciences Physiques (IMSP), Université de Porto-Novo, 01 BP 613, Porto-Novo, Bénin

    M. G. Ganiou, Ines G. Salako, M. J. S. Houndjo & J. Tossa

  2. Département de Physique, Université d’Agriculture de Kétou, BP 13, Kétou, Bénin

    Ines G. Salako

  3. Faculté des Sciences et Techniques de Natitingou (FAST), Université de Natitingou, BP 72, Natitingou, Bénin

    M. J. S. Houndjo

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Ganiou, M.G., Salako, I.G., Houndjo, M.J.S. et al. Geodesic Deviation Equation in ΛCDM \(f(T,\mathcal {T})\) Gravity. Int J Theor Phys 55, 3954–3972 (2016). https://doi.org/10.1007/s10773-016-3025-8

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