Galactic rotation dynamics in a new $f(\mathcal{R})$ gravity model

TL;DR

This paper tests a new $f( abla)$ gravity model's ability to explain galactic rotation curves and the Tully-Fisher relation, showing it can account for observations without dark matter.

Contribution

It introduces and tests a novel $f( abla)$ gravity model at galactic scales, demonstrating its compatibility with observed rotation curves and the Tully-Fisher relation.

Findings

Model fits well with observed galaxy rotation curves.

The model explains flat rotation curves without dark matter.

Consistent with the Tully-Fisher relation across samples.

Abstract

We propose to test the viability of the recently introduced $f(\mathcal{R})$ gravity model in the galactic scales. For this purpose we consider test particles moving in stable circular orbits around the galactic center. We study the Palatini approach of $f(\mathcal{R})$ gravity via Weyl transformation, which is the frame transformation from the Jordan frame to the Einstein frame. We derive the expression of rotational velocities of test particles in the new $f(\mathcal{R})$ gravity model. For the observational data of samples of high surface brightness and low surface brightness galaxies, we show that the predicted rotation curves are well fitted with observations, thus implying that this model can explain flat rotation curves of galaxies. We also study an ultra diffuse galaxy, AGC $242019$ which has been claimed in literature to be a dark matter dominated galaxy similar to low surface brightness galaxies with a slowly rising rotation curve. The rotation curve of this galaxy also fits well with the model prediction in our study. Furthermore, we studied the Tully-Fisher relation for the entire sample of galaxies and found that the model prediction shows the consistency with the data.