Method of N-body simulation on the MOdified Gravity

Abstract: Scalar Tensor Vector Gravity(STVG) is one of a modified gravity theory developed by John Moffat(2005). MOG is abbreviated name for this theory.This theory is added a massive vector field to Brans-Dicke theory. It can explain a galactic rotary curve and the structure formation without dark matter. Without dark energy,acceleration universe too. However,these are claims by the developer and collaboraters.This theory was only inspected by simple approximate calculation. Therefore it needs more objective verifications.We will carried out verification from the viewpoint of N-body simulation. Such study is already accomplished by Brandao(2010).However, they did not precisely formulate N-body simulation on MOG. This paper shows formulation of the N-body simulation on MOG more precisely.