A Model of f (R) Gravity as an Alternative for Dark Matter in Spiral Galaxies

Abstract

In this paper we study consistent solutions of spherically symmetric space in metric ) (R f gravity theory. Here we inversely obtain a generic action from metric solutions that describe flat rotation curves in spiral galaxies without dark matter. Then we show that obtained solutions are in conformity with Tully-Fisher relation and modified Newtonian dynamics, which are two strong constraints in justification of flat rotation curves in spiral galaxies.

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.…”

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.…”