Constraints on $R^n$ gravity from precession of orbits of S2-like stars

TL;DR

This paper investigates how $R^n$ gravity affects the orbits of stars near the Galactic center, proposing observational constraints based on orbital precession measurements from current and future telescopes.

Contribution

It provides the first detailed analysis of $R^n$ gravity effects on S2-like star orbits and derives constraints on the model parameters from orbital precession data.

Findings

Most probable $r_c$ parameter is ~100 AU.

Universal parameter $eta$ is close to 0.01.

Orbit precession is opposite to General Relativity, similar to Newtonian with matter distribution.

Abstract

We study some possible observational signatures of $R^n$ gravity at Galactic scales and how these signatures could be used for constraining this type of $f(R)$ gravity. For that purpose, we performed two-body simulations in $R^n$ gravity potential and analyzed the obtained trajectories of S2-like stars around Galactic center, as well as resulting parameter space of $R^n$ gravity potential. Here, we discuss the constraints on the $R^n$ gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparison between the theoretical results and observations. Our results show that the most probable value for the parameter $r_c$ in $R^n$ gravity potential in the case of S2-like stars is $\sim$100 AU, while the universal parameter $\beta$ is close to 0.01. Also, the $R^n$ gravity potential induces the precession of S2-like stars orbit in opposite direction with respect to General Relativity, therefore, such a behavior of orbits qualitatively is similar to a behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).