Dark matter density profile and galactic metric in Eddington-inspired Born-Infeld gravity

TL;DR

This paper investigates the density profile and gravitational metric of dark matter halos within Eddington-inspired Born-Infeld gravity, providing numerical and approximate analytical solutions consistent with observed galactic rotation curves.

Contribution

It introduces a novel application of EiBI gravity to model dark matter halos, deriving density profiles and metrics that align with galactic observations.

Findings

Dark matter density follows a non-singular Lane-Emden profile with polytropic index 1.

The parameter κ is constrained to match realistic dark matter halo properties.

The theory reproduces expected gravitational behavior in the Newtonian limit.

Abstract

We consider the density profile of pressureless dark matter in Eddington-inspired Born-Infeld (EiBI) gravity. The gravitational field equations are investigated for a spherically symmetric dark matter galactic halo, by adopting a phenomenological tangential velocity profile for test particles moving in stable circular orbits around the galactic center. The density profile and the mass distribution, as well as the general form of the metric tensor is obtained by numerically integrating the gravitational field equations, and in an approximate analytical form by using the Newtonian limit of the theory. In the weak field limit the dark matter density distribution is described by the Lane-Emden equation with polytropic index $n=1$, and is non-singular at the galactic center. The parameter $\kappa $ of the theory is determined so that that the theory could provide a realistic description of the dark matter halos. The gravitational properties of the dark matter halos are also briefly discussed in the Newtonian approximation.