Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl gravity

TL;DR

This paper establishes an upper limit on dark matter central density in EiBI gravity, using Weyl gravity inputs, and finds that observed densities in galaxies conform to this theoretical constraint, supporting EiBI's predictions.

Contribution

It introduces a novel method to constrain dark matter density in EiBI gravity using Weyl gravity parameters and verifies these constraints against galactic data.

Findings

Dark matter densities in galaxies obey an upper limit proportional to the inverse square of the halo radius.

The density interval between lower and upper bounds aligns well with observed values in LSB galaxies.

The existence of a stability-induced upper density limit is a key prediction of EiBI gravity.

Abstract

Recently, Harko et al. (2014) derived an approximate metric of the galactic halo in the Eddington inspired Born-Infeld (EiBI) gravity. In this metric, we show that there is an upper limit $\rho _{0}^{\text{upper}}$ on the central density $\rho _{0}$ of dark matter such that stable circular orbits are possible only when the constraint $\rho _{0}\leq \rho_{0}^{\text{upper}}$ is satisfied in each galactic sample. To quantify different $\rho _{0}^{\text{upper}}$ for different samples, we follow the novel approach of Edery & Paranjape (1998), where we use as input the geometric halo radius $R_{\text{WR}}$ from Weyl gravity and equate it with the dark matter radius $R_{\text{DM}}$ from EiBI gravity for the same halo boundary. This input then shows that the known fitted values of $\rho _{0}$ obey the constraint $\rho_{0}\leq\rho_{0}^{\text{upper}}\propto $ ($R_{\text{WR}}$)$^{-2}$. Using the mass-to-light ratios giving $\alpha $, we shall also evaluate $\rho _{0}^{\text{lower}}$ $\propto $ $(\alpha -1)M_{\text{lum}}R_{\text{WR}}^{-3}$ and the average dark matter density $\left\langle \rho\right\rangle ^{\text{lower}}$. Quantitatively, it turns out that the interval $\rho _{0}^{\text{lower}}$ $\leq \rho _{0}\leq $ $\rho _{0}^{\text{upper}}$ verifies reasonably well against many dark matter dominated low surface brightness (LSB) galaxies for which values of $\rho _{0}$ are independently known. The interval holds also in the case of Milky Way galaxy. Qualitatively, the existence of a stability induced upper limit $\rho _{0}^{\text{upper}}$ is a remarkable prediction of the EiBI theory.