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

Understand

Alternative theories of gravity may serve to overcame several shortcomings of the standard cosmological model but, in their weak field limit, General Relativity must be recovered so as to match the tight constraints at the Solar System scale.

• Therefore, testing such alternative models at scales of stellar systems could give a unique opportunity to confirm or rule them out.
• One of the most straightforward modifications is represented by analytical $f(R)$-gravity models that introduce a Yukawa-like modification to the Newtonian potential thus modifying the dynamics of particles.
• Using the geodesics equations, we have illustrated the amplitude of these modifications.