Is MOND an effect of cosmic frame-dragging à la Mach?

Abstract

The physical origin of modified Newtonian dynamics (MOND), which predicts galaxy rotation curves via a single empirical acceleration constant a0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_0$$\end{document} without the need for dark matter, remains unknown. I propose an origin of MOND’s interpolating function and a0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_0$$\end{document} as modified inertia within a framework closely related to gravitoelectromagnetism, the linearized limit of General Relativity. Building on Sciama’s model unifying gravity and inertia, which implements Mach’s principle and the relativity of acceleration through gravitoelectric induction, I consider an idealized homogeneous universe undergoing constant Hubble expansion. I identify a0∼H02Ru∼c2/Ru\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_0 \sim H_0^2R_u \sim c^2/R_u$$\end{document} with the relative recession acceleration of cosmic matter near the horizon, which dominates the cosmological contribution. I show that this scale enters local inertial dynamics only when the relative acceleration of the universe becomes anisotropic and the Rindler horizon is comparable to the cosmic Hubble horizon, at accelerations of order a0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_0$$\end{document} and below. By the simplest Ansatz for the observer’s acceleration-dependent causal volume, accounting for the interplay between the Hubble horizon and the associated Rindler horizon, I obtain a correction to inertia resembling MOND’s interpolating function after an order-unity normalization of a cosmological coefficient. Physically, the region brought into causal connection ahead of the accelerating observer by the deformation of the cosmic horizon contributes less inertial drag than is lost from the region removed behind him by the Rindler horizon. This proof of concept motivates the possibility that MOND arises from large-scale linear inertial frame-dragging induced by the expanding universe within General Relativity.