Precession shift in curvature based Extended Theories of Gravity and Quintessence fields

TL;DR

This paper uses planetary precession data to constrain parameters of extended gravity theories and quintessence fields, improving bounds on hypothetical weak forces and exploring modifications to gravitational potentials.

Contribution

It introduces new constraints on Yukawa-like and power-law gravitational potentials within extended gravity models using planetary precession data.

Findings

Precession data constrains Yukawa potential parameters significantly.

Bounds on the force range parameter ${eta}$ are improved by several orders of magnitude.

Analysis of quintessence-induced modifications to Schwarzschild geometry is presented.

Abstract

In this paper we constrain the sizes of hypothetical new weak forces by making use the data coming from the precession of Planets. We consider the weak field approximation of Scalar-Tensor Fourth Order Gravity (STFOG), which include several models of modified gravity. The form of the corrections to the Newtonian potential if of the form of Yukawa-like potential (5th force), i.e. $V(r) = {\alpha} \dfrac{e^{-\beta r}}{r}$, where ${\alpha}$ is the parameter related to the strength of the potential, and ${\beta}$ to the range of the force. The present data on periastron advance allow to infer a constraint on the free parameter of the gravitational models. Moreover, the Non-Commutative Spectral Gravity (NCSG) is also studied, being a particular case STFOG. Here we show that the precession shift of Planet allows to improve the bounds on parameter ${\beta}$ by several orders of magnitude. Finally such an analysis is studied to the case of power-like potential, referring in particular to deformation of the Schwarzschild geometry induced by a quintessence field, responsible of the present accelerated phase of the Universe.