Randers geometry as MOND/dark matter

TL;DR

This paper develops a relativistic gravity theory based on Randers geometry that reproduces MOND and dark matter effects, aligns with cosmological observations, and predicts testable deviations in post-Newtonian parameters.

Contribution

It introduces a second-order relativistic gravity model based on Randers geometry that unifies MOND, dark matter effects, and the cosmological constant within a consistent framework.

Findings

Reproduces MOND and dark matter phenomena in a relativistic setting.

Predicts a few percent deviation in the post-Newtonian parameter γ.

Compatible with current observations and testable with future data.

Abstract

We consider a deviation of the physical length from the Riemann geometry toward the Randers'. We construct a consistent second-order relativistic theory of gravity that dynamically reduces to the Einstein-Hilbert theory for the strong and Newtonian gravity while its weak gravitational regime reproduces MOND and the gravitational lensing attributed to the dark matter halo. It also naturally accommodates the observed value of the cosmological constant. We show that it predicts a few percent deviation for the post Newtonian parameter $\gamma$ in a part of the regime that interpolates the Newtonian regime to the MOND regime. The deviation is consistent with the reported observations but can possibly be detected by fine-tuned refinements of the current data or specified future observations.