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

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).

12 pages, 12 figures, accepted in Phys. Rev. D

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• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Analysis of Rotation Curves in the framework of R^n gravity
• Orbital precession due to central-force perturbations
• Solar system constraints on R${}^n$ gravity
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• Gravitational lensing in fourth order gravity
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Cited by in corpus (9)

• Testing General Relativity with stellar orbits around the supermassive black hole in our Galactic center
• Constraints on $R^n$ gravity from precession of orbits of S2-like stars: a case of a bulk distribution of mass
• Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
• Towards an observational test of black hole versus naked singularity at the galactic center
• Testing modified gravity via Yukawa potential in two body problem: Analytical solution and observational constraints
• Testing the Galactic Centre potential with S-stars
• The generalized second law of thermodynamics for interacting $f(R)$ gravity
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Tests of gravity theories with Galactic Center observations