A well-behaved f(R) gravity model in planetary motions

Abstract

a b s t r a c tIn this paper we consider asymptotic behavior of a hybrid action of f(R) gravity model which proposed by Saffari and Rahvar (2008), in the Solar system scale, which can explain Pioneer anomalous acceleration. We use the resultant weak field gravitational potential which comes from the hybrid action to test its impacts on the Solar system dynamics, by comparing theoretical precession of perihelion of a test particle, _ $, with corrections to the standard Newtonian-Einstenian precessions of perihelia of some planets, which recently estimated by Pitjeva (2005aPitjeva ( ,b, 2006Pitjeva ( , 2008. Here we show that the asymptotic behavior of hybrid action is in more accordance with observation relative to the other modifications such as power law and logarithmic corrections (Iorio, 2008). We also show that an extra additional lensing of the prediction of General Relativity is reproduced. Finally we consider the stability condition of planetary orbits in the presence of the hybrid action.

A viable logarithmicf(R) model for inflation

“…Other examples of logarithmic f (R) models can be found in refs. [12,13,[23][24][25][26][27][28][29][30][31][32][33][34][35][36] and for examples of f (R) inflationary models, check [2,10,11,29,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and the references therein.…”

Dark Energy Constraints on Red-Shift-Based Gravity

“…Particularly, we are interested in fourth order theories [43][44][45][46][47][48][49][50][51][52][53][54][55] based on replacing the scalar curvature in the Hilbert-Einstein action with a generic analytic function ( ) which should be reconstructed starting from data and physically motivated issues. These models fit both the cosmological data and Solar System constraints in several physically interesting cases [56][57][58][59][60][61][62][63][64][65]. Vacuum solutions of ( ) gravity theories is one of interesting subjects which are obtained for constant Ricci scalar [66][67][68][69][70][71][72], allowing derivation of non constant curvature scalar vacuum solutions.…”

Vacuum solution of a linear red-shift based correction in f (R) gravity

“…In particular, we will be interested here in fourth order theories [42][43][44][45][46][47][48][49][50][51][52][53][54] based on replacing the scalar curvature R in the Hilbert-Einstein action with a generic analytic function f (R) which should be reconstructed starting from data and physically motivated issues. Also referred to as f (R) gravity, these models have been shown to be able to fit both the cosmological data and Solar System constraints in several physically interesting cases [55][56][57][58][59][60][61][62][63][64]. These theories are also referred to as 'extended theories of gravity', since they naturally generalize General Relativity.…”