Generalized Mattig's relation in Brans-Dicke-Rastall gravity

Abstract

The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $\eta(z)$ and observer area distance $r_0(z)$ and compare the results with $\Lambda$CDM model.