Analysis of the Yukawa gravitational potential in f(R) gravity. I. Semiclassical periastron advance

Abstract

The concordance cosmological model has been successfully tested over the last decades. Despite its successes, the fundamental nature of dark matter and dark energy is still unknown. Modifications of the gravitational action have been proposed as an alternative to these dark components. The straightforward modification of gravity is to generalize the action to a function, f (R), of the scalar curvature. Thus one is able to describe the emergence and the evolution of the Large Scale Structure without any additional (unknown) dark component. In the weak field limit of the f (R)-gravity, a modified Newtonian gravitational potential arises. This gravitational potential accounts for an extra force, generally called fifth force, that produces a precession of the orbital motion even in the classic mechanical approach. We have shown that the orbits in the modified potential can be written as Keplerian orbits under some conditions on the strength and scale length of this extra force. Nevertheless, we have also shown that this extra term gives rise to the precession of the orbit. Thus, comparing our prediction with the measurements of the precession of some planetary motions, we have found that the strength of the fifth force must be in the range [2.70 − 6.70] × 10 −9 with the characteristic scale length to fix to the fiducial values of ∼ 5000 AU.

Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds

“…Clearly, that forthcoming data analysis of LARES data will improve LAGEOS constraints on Yukawa theory parameters [35][36][37]. Toy models with the Yukawa potential derived in f (R) gravity have been considered for Solar System and the Galactic Center and it was shown how to evaluate Yukawa potential parameters from observations for these systems [39,40]. Yukawa potential have been successfully used to fit observational data for galactic rotation curves and clusters of galaxies [41][42][43].…”

Screening of a charged impurity in graphene in a magnetic field

“…Naively, one would think that the supercritical regime in this problem sets in when the lowest-energy electron bound level intersects the highest energy hole bound state at E = 0. However, it was found [21] that the levels first approach each other as the dipole moment increases, and then diverge. In fact, this behavior is typical for an avoided crossing [23] of the states with the same symmetry.…”

“…An interesting problem of two oppositely charged impurities was considered in Refs. [21,22]. Obviously, this dipole problem is particle-hole symmetric and electron states are symmetric with respect to the change of the sign of energy, E → −E.…”

Linearized modified gravity theories and gravitational waves physics in the GBD theory

“…According to Eqs. (19)(20)(21)(22) and using the relation θ = η µν θ µν = − 4m φ0Φ0 1 r , we obtain the non-vanishing components of the metric perturbation term as follows…”

“…Studies on the modified gravity theories of GR has been always a hot area. Several modified gravity theories have been widely studied [14][15][16][17][18][19][20][21][22], especially two simple modifications to GR: the f (R) theory [23,24] and the Brans-Dicke (BD) theory [25]. In the BD theory, a scalar field φ can be introduced naturally by defining φ(t) = 1/G(t).…”