Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl 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 ${\rho }_0\le {\rho }_0^{\text{upper}}$ 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 ${\rho }_0\le {\rho }_0^{\text{upper}}\propto$ ($R_{\text{WR}}$)${}^{-2}$. 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 ${⟨\rho ⟩}^{\text{lower}}$. Quantitatively, it turns out that the interval ${\rho }_0^{\text{lower}}$ $\le {\rho }_0\le$ ${\rho }_0^{\text{upper}}$ 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.

37 pages, 6 figures

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