Field equations and cosmology for a class of nonlocal metric models of MOND

TL;DR

This paper derives full field equations for nonlocal modified gravity models aimed at reproducing galaxy rotation curves without dark matter, analyzing their cosmological implications and fitting expansion history.

Contribution

It provides the complete field equations for a class of nonlocal MOND-inspired gravity models and explores their cosmological solutions and parameter fitting.

Findings

Derived full field equations for nonlocal MOND models.

Analyzed cosmological solutions with fixed and variable MOND acceleration.

Discussed fitting free functions to match the universe's expansion history.

Abstract

We consider a class of nonlocal, pure-metric modified gravity models which were developed to reproduce the Tully-Fisher relation without dark matter and without changing the amount of weak lensing predicted by general relativity. Previous work gave only the weak field limiting form of the field equations specialized to a static and spherically symmetric geometry. Here we derive the full field equations and specialize them to a homogeneous, isotropic and spatially flat geometry. We also discuss the problem of fitting the free function to reproduce the expansion history. Results are derived for models in which the MOND acceleration a_0 ~ 1.2 x 10^{-10} m/s^{2} is a fundamental constant and for the more phenomenologically interesting case in which the MOND acceleration changes with the cosmological expansion rate.