Analysis of the Yukawa gravitational potential in $f(R)$ gravity II: relativistic periastron advance.
Alternative theories of gravity may serve to overcame several shortcomings of the standard cosmological model but, in their weak field limit, they must recover General Relativity to match the tight constraints at Solar System scale. Therefore, testing such alternative models at scale 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 that modify the dynamics of particles. Using the geodesic equations, we have illustrated the amplitude of these modifications. First, we have numerically integrated the equations of motion showing the orbital precession of a particle around a massive object. Second, we have computed an analytic expression for the periastron advance of systems having semi-major axis much lower than the Yukawa-scale length. Finally, we have extended our results to the case of a binary system composed of two massive objects. Our analysis provides a powerful tool to obtain constraints on the underlying theory of gravity using current and forthcoming dataset.
Publisher URL: http://arxiv.org/abs/1801.08136