Galaxy rotation curves from a fourth order gravity

TL;DR

This paper proposes a fourth order gravity modification to the Poisson equation that can explain flat galaxy rotation curves without dark matter, aligning with observations and suggesting potential theoretical origins.

Contribution

It introduces a novel fourth order gravity model that reproduces Yukawa-type modifications similar to STVG, explaining galaxy rotation curves with specific parameter choices.

Findings

The modified Poisson equation fits galaxy rotation data.

The model aligns with Yukawa-type gravity modifications.

Potential origins include higher-order gravity theories or galaxy interactions.

Abstract

While the standard and most popular explanation for the flatness of galaxy rotation curves is dark matter, one cannot at this stage rule out an explanation based on a modified law of gravitation, which agrees with Newtonian gravitation on the scale of the solar system, but differs from it on larger length scales. Examples include Modfied Newtonian Dynamics [MOND] and Scalar-Tensor-Vector Gravity [STVG]. Here we report on a fourth order modification of the Poisson equation which yields the same Yukawa type modification of Newtonian gravity as STVG, and which can explain flat galaxy rotation curves for a large sample of galaxies, once specific values for two parameters have been chosen. We speculate on two possible origins for this modified Poisson equation: first, a possible fourth order modification of general relativity, and second, quadrupole gravitational polarization induced on a galaxy because of the pull of neighbouring galaxies.