Analysis of the Yukawa gravitational potential in $f(R)$ gravity I: semiclassical periastron advance

Abstract

The {\it concordance} cosmological model has been successfully tested throughout the last decades. Despite its successes, the fundamental nature of dark matter and dark energy is still unknown. Modifications of the gravitational action have been proposed as an alternative to these dark components. The straightforward modification of gravity is to generalize the action to a function, $f(R)$, of the scalar curvature. Thus one is able to describe the emergence and the evolution of the Large Scale Structure without any additional (unknown) dark component. In the weak field limit of the $f(R)$-gravity, a modified Newtonian gravitational potential arises. This gravitational potential accounts for an extra force, generally called fifth force, that produces a precession of the orbital motion even in the classic mechanical approach. We have shown that the orbits in the modified potential can be written as Keplerian orbits under some conditions on the strength and scale length of this extra force. Nevertheless, we have also shown that this extra term gives rise to the precession of the orbit. Thus, comparing our prediction with the measurements of the precession of some planetary motions, we have found that the strength of the fifth force must be in the range $[2.70-6.70]\times 10^{-9}$ whit the characteristic scale length to fixed to the fiducial values of $\sim 5000$ AU.

9 pages, 5 figures, accepted for publication in Phys. Rev. D

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• Modified gravity revealed along geodesic tracks
• Constraining Non-local Gravity by S2 star orbits
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• Testing modified gravity via Yukawa potential in two body problem: Analytical solution and observational constraints
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• Limiting the Yukawa Gravity through the Black Hole Shadows of Sgr A* and M87*
• Metric tensor at second perturbation order for spherically symmetric space-times
• Yukawa-Casimir Wormholes