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

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.

14 pages, 6 figures. The title has been changed in this version

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• Magnetic Suppression of Cosmic Rays' Flux in $\mathbf{f}(\mathbf{R})$ and $\mathbf{f}(\mathbf{Q})$ Theories of Gravity
• Galactic dynamics in the presence of scalaron: A perspective from $\mathbf{f}(\mathbf{R})$ gravity
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy
• Investigating the effects of gravitational lensing by Hu-Sawicki $\mathbf{f}(\mathbf{R})$ gravity black holes
• Modelling Cosmic Rays Flux with Pierre Auger and Telescope Array Data in $\mathbf{f}(\mathbf{R})$ and $\mathbf{f}(\mathbf{Q})$ Theories of Gravity
• Ultra-high energy cosmic rays with UFA-15 source model in Bumblebee gravity theory