Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity
  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. 
M. G. Ganiou (Benin, IMSP), Ines G. Salako (Benin, IMSP & Ketou U.),   M. J. S. Houndjo (Benin, IMSP & Natitingou U.), J. To...
gr-qc