$f(R)$ gravity in the solar system and cosmological scalarons (2406.00351v3)

Abstract: Since last two decades $f(R)$ gravity theory has been extensively used as a serious alternative of general relativity to mimic the effects of dark energy. The theory presents a Yukawa correction to Newtonian gravitational potential, acting as a fifth force of Nature. Generally speaking, this new force is mediated by a scalar field known as scalaron. It affects orbital dynamics of test bodies around a central mass. When the scalaron becomes massive $f(R)$ gravity reduces to Newtonian theory in the weak field limit. In this paper we investigate scalaron mass in the solar system through existing measurements of perihelion shift of planets, Cassini's measurement of the Parametrized Post Newtonian parameter and measurement of the Brans-Dicke coupling constant. The scalaron mass is constrained in the range ($9.29\times 10^{-18}-5.64\times 10^{-16}$) eV. Our results are consistent with existing constraints on the theory arising from the environment of the Galactic Center black hole and binary pulsar systems. Scalarons realized in the solar system are reproduced in the radiation era (($0.88-53.89$) sec) of the universe with a time varying scalaron mass.