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arXiv · 1601.02895

Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity

M. G. Ganiou·Ines G. Salako·M. J. S. Houndjo·J. Tossa
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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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M. G. Ganiou, Ines G. Salako, M. J. S. Houndjo, J. Tossa. 2015-12-31. Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity. https://doi.org/10.1007/s10773-016-3025-8

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