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

TL;DR

This paper derives a generalized Mattig's relation within Brans-Dicke-Rastall gravity by formulating and numerically solving the Geodesic Deviation Equation for FLRW spacetime, comparing results with the standard CDM model.

Contribution

It introduces a new formulation of the Geodesic Deviation Equation in Brans-Dicke-Rastall gravity and derives a generalized Mattig's relation for this theory.

Findings

Derived the GDE for FLRW in Brans-Dicke-Rastall gravity

Numerically solved null vector GDE to obtain deviation and distance measures

Compared the generalized Mattig relation with CDM results

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.