Galaxy rotation curves and preferred reference frame effects

As an alternative to dark matter models we use generalized Jordan–Brans–Dicke scalar–vector–tensor (JBD-SVT) gravity model to study the behavior of the rotational velocities of test particles moving around galaxies. To do so we consider an interaction potential U(ϕ,Nμ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(\phi ,N_{\mu })$$\end{document} between the Brans–Dicke scalar field ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document} and time like dynamical four-vector field Nμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_\mu $$\end{document} which plays as four velocity of a preferred reference frame. We show that at in weak field limits metric solution of the galaxy under consideration reaches to a modified Schwarzschild–de Sitter space in which mass of the vector field plays as an effective cosmological constant. In fact the present work proposes modification on the formulation of Newton’s gravitational acceleration. This is used to explain circular velocity of galaxies without postulating dark matter. We also check our theoretical results with empirical baryonic Tully Fisher relation which states a linear relations between the rotational speed of galaxies and their mass. Mathematical calculation predict a good correspondence between our theoretical results and experimental observations for a set of 12 spiral galaxies.