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Register a new userUpper Limit on the Central Density of Dark Matter in the Eddington inspired Born-Infield (EiBI) Gravity
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We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko textit{et al.} (2014). It turnsout that stability depends more strongly on the dark matter central density $%rho_{0}$ than on other parameters of the solution. This property then yields an upper limit on $rho _{0}$ for each individual galaxy, which we call here $rho _{0}^{text{upper}}$, such that stable circular orbits are possible textit{only} when the constraint $rho _{0}leq rho _{0}^{text{upper}}$ is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius $R_{text{DM}}sim 180$ kpc and find that $rho _{0}^{text{upper}}sim 2.37times 10^{11}$ $M_{odot }$kpc$^{-3}$. This limit turns out to be about four orders of magnitude larger than the latest data on central density $rho _{0}$ arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the EiBI solution could qualify as yet another viable alternative model for dark matter.
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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}leqrho_{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 $leftlangle rhorightrangle ^{text{lower}}$. 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.
In this paper, we wish to investigate certain observable effects in the recently obtained wormhole solution of the EiBI theory, which generalizes the zero mass Ellis-Bronnikov wormhole of general relativity. The solutions of EiBI theory contain an extra parameter $kappa$ having the inverse dimension of the cosmological constant $Lambda$, and is expected to modify various general relativistic observables such as the masses of wormhole mouths, tidal forces and light deflection. A remarkable result is that a non-zero $kappa$ could prevent the tidal forces in the geodesic orthonormal frame from becoming arbitrarily large near a small throat radius $(r_0 sim {0})$ contrary to what happens near a small Schwarzschild horizon radius $(M sim 0)$. The role of $kappa$ in the flare-out and energy conditions is also analysed, which reveals that the energy conditions are violated. We show that the exotic matter in the EiBI wormhole cannot be interpreted as phantom $({omega}=(p_{r}/ rho)<-1)$ or ghost field ${phi} $ of general relativity due to the fact that both $rho$ and $p_{r}$ are negative for all $kappa$.
We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI) gravity. We show that this bound depends on an energy condition controlled by the model parameter $kappa$. From this bound, we can constrain $kappalesssim 10^{8}text{m}^2$ if a neutron star with a mass around $3M_{odot}$ is observed in the future. In addition, to avoid the potential pathologies in EiBI, a emph{Hagedorn-like} equation of state associated with $kappa$ at the center of a compact star is inevitable, which is similar to the Hagedorn temperature in string theory.
We investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic inflation. For long wave-length modes, the perturbation exhibits a peculiar rise in the power spectrum which may leave a signature in the cosmic microwave background radiation.
We construct an axially symmetric solution of Eddington-inspired Born-Infeld gravity coupled to an electromagnetic field in 2+1 dimensions including a (negative) cosmological constant term. This is achieved by using a recently developed mapping procedure that allows to generate solutions in certain families of metric-affine gravity theories starting from a known seed solution of General Relativity, which in the present case corresponds to the electrically charged Banados-Teitelboim-Zanelli (BTZ) solution. We discuss the main features of the new configurations, including the modifications to the ergospheres and horizons, the emergence of wormhole structures, and the consequences for the regularity (or not) of these space-times via geodesic completeness.
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