https://doi.org/10.1140/epjc/s10052-022-10235-x
Regular Article - Theoretical Physics
Precession shift in curvature based extended theories of gravity and quintessence fields
1
Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, via G. Paolo II, 84084, Fisciano, Italy
2
Istituto Nazionale di Fisica Nucleare (INFN), Gruppo collegato di Salerno, via G. Paolo II, 84084, Fisciano, Italy
Received:
7
October
2021
Accepted:
20
March
2022
Published online:
2
April
2022
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. 
, where 
is the parameter related to the strength of the potential, and 
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 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.
© The Author(s) 2022
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