Extended galactic rotational velocity profiles in f(R) gravity background

Abstract

AbstractAn attempt has been made to explore the geometric effects of f(R) action on the galactic dynamics under the weak field approximation. The rotational velocity is calculated beyond the Einstein’s geometric theory of gravity. It is inspired by the cosmological geometric relation obtained in the power-law f(R) gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein–Hilbert gravity action (taking R as $$f(R)\propto R^{1+\delta }$$f(R)∝R1+δ) at the galactic scales for the explanation of the flatness paradox associated with the clustered galactic dark matter. We obtain the contribution of a dynamical f(R) cosmological background geometry on accelerating the test mass. Furthermore, the integrated effective acceleration of the test mass due to a massive spherically symmetric source in f(R) background is calculated via the study of geodesics for the suitable spacetime metric and an equation for the effective rotational velocity has been developed. We test the viability of the proposed model by tracing the motion of a test mass far from the disk of galactic matter for smaller $$\delta $$δ. The possible galactic rotational velocity curves in f(R) background are discussed for the formula obtained with $$\delta<< 1$$δ<<1. We also obtain constraints on $$\delta $$δ$$O(10^{-6})$$O(10-6) confirmed by observations.