Galactic metric, dark radiation, dark pressure and gravitational lensing in brane world models

In the braneworld scenario, the four dimensional effective Einstein equation has extra terms which arise from the embedding of the 3-brane in the bulk. These non-local effects, generated by the free gravitational field of the bulk, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center, which is usually explained by postulating the existence of the dark matter. We obtain the exact galactic metric, the dark radiation and the dark pressure in the flat rotation curves region in the brane world scenario. Due to the presence of the bulk effects, the flat rotation curves could extend several hundred kpc. The limiting radius for which bulk effects are important is estimated and compared with the numerical values of the truncation parameter of the dark matter halos, obtained from weak lensing observations. There is a relatively good agreement between the predictions of the model and observations. The deflection of photons is also considered and the bending angle of light is computed. The bending angle predicted by the brane world models is much larger than that predicted by standard general relativistic and dark matter models. The angular radii of the Einstein rings are obtained in the small angles approximation. The predictions of the brane world model for the tangential shear are compared with the observational data obtained in the weak lensing of galaxies in the Red-Sequence Cluster Survey. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the different dynamical laws proposed to model the motion of particles at the galactic level and the standard dark matter models.Comment: 33 pages, 3 figures, accepted for publication in Ap

Generalized virial theorem in Palatini f(R)f(R) gravity

We use the collision-free Boltzmann equation in Palatini $f({\mathcal{R}})$ gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contribute to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in cluster of galaxies. We then derive the velocity dispersion relation for clusters followed by the metric tensor components inside the cluster as well as the $f({\mathcal{R}})$ lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the $f({\mathcal{R}})$ virial theorem is a convenient tool to test the viability of $f({\mathcal{R}})$ theories in different models. Finally, we discuss the limitations of our approach in the light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work.Comment: 16 pages, to appear in PR

The virial theorem and the dynamics of clusters of galaxies in the brane world models

A version of the virial theorem, which takes into account the effects of the non-compact extra-dimensions, is derived in the framework of the brane world models. In the braneworld scenario, the four dimensional effective Einstein equation has some extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. To derive the generalized virial theorem we use a method based on the collisionless Boltzmann equation. The dark radiation term generates an equivalent mass term (the dark mass), which gives an effective contribution to the gravitational energy. This term may account for the well-known virial theorem mass discrepancy in actual clusters of galaxies. An approximate solution of the vacuum field equations on the brane, corresponding to weak gravitational fields, is also obtained, and the expressions for the dark radiation and dark mass are derived. The qualitative behavior of the dark mass is similar to that of the observed virial mass in clusters of galaxies. We compare our model with the observational data for galaxy clusters, and we express all the physical parameters of the model in terms of observable quantities. In particular, we predict that the dark mass must extend far beyond the presently considered virial radius. The behavior of the galaxy cluster velocity dispersion in brane world models is also considered. Therefore the study of the matter distribution and velocity dispersion at the extragalactic scales could provide an efficient method for testing the multi-dimensional physical models.Comment: 29 pages, no figures, accepted for publication in PR

Bayes-X: a Bayesian inference tool for the analysis of X-ray observations of galaxy clusters

We present the first public release of our Bayesian inference tool, Bayes-X, for the analysis of X-ray observations of galaxy clusters. We illustrate the use of Bayes-X by analysing a set of four simulated clusters at z=0.2-0.9 as they would be observed by a Chandra-like X-ray observatory. In both the simulations and the analysis pipeline we assume that the dark matter density follows a spherically-symmetric Navarro, Frenk and White (NFW) profile and that the gas pressure is described by a generalised NFW (GNFW) profile. We then perform four sets of analyses. By numerically exploring the joint probability distribution of the cluster parameters given simulated Chandra-like data, we show that the model and analysis technique can robustly return the simulated cluster input quantities, constrain the cluster physical parameters and reveal the degeneracies among the model parameters and cluster physical parameters. We then analyse Chandra data on the nearby cluster, A262, and derive the cluster physical profiles. To illustrate the performance of the Bayesian model selection, we also carried out analyses assuming an Einasto profile for the matter density and calculated the Bayes factor. The results of the model selection analyses for the simulated data favour the NFW model as expected. However, we find that the Einasto profile is preferred in the analysis of A262. The Bayes-X software, which is implemented in Fortran 90, is available at http://www.mrao.cam.ac.uk/facilities/software/bayesx/.Comment: 22 pages, 11 figure

Effects of a multi-component exercise program and calcium–vitamin-D3-fortified milk on bone mineral density in older men : a randomised controlled trial

Summary We examined the independent and combined effects of a multi-component exercise program and calcium&ndash;vitamin-D3-fortified milk on bone mineral density (BMD) in older men. Exercise resulted in a 1.8% net gain in femoral neck BMD, but additional calcium&ndash;vitamin D3 did not enhance the response in this group of older well-nourished men.Introduction This 12-month randomised controlled trial assessed whether calcium&ndash;vitamin-D3-fortified milk could enhance the effects of a multi-component exercise program on BMD in older men.Methods Men (n&thinsp; =&thinsp;180) aged 50&ndash;79 years were randomised into: (1) exercise + fortified milk; (2) exercise; (3) fortified milk; or (4) controls. Exercise consisted of high intensity progressive resistance training with weight-bearing impact exercise. Men assigned to fortified milk consumed 400 mL/day of low fat milk providing an additional 1,000 mg/day calcium and 800 IU/day vitamin D3. Femoral neck (FN), total hip, lumbar spine and trochanter BMD and body composition (DXA), muscle strength 25-hydroxyvitamin D and parathyroid hormone (PTH) were assessed.Results There were no exercise-by-fortified milk interactions at any skeletal site. Exercise resulted in a 1.8% net gain in FN BMD relative to no-exercise (p&thinsp;&lt;&thinsp;0.001); lean mass (0.6 kg, p&thinsp;&lt;&thinsp;0.05) and muscle strength (20&ndash;52%, p&thinsp;&lt;&thinsp;0.001) also increased in response to exercise. For lumbar spine BMD, there was a net 1.4&ndash;1.5% increase in all treatment groups relative to controls (all p&thinsp;&lt;&thinsp;0.01). There were no main effects of fortified milk at any skeletal site.Conclusion A multi-component community-based exercise program was effective for increasing FN BMD in older men, but additional calcium&ndash;vitamin D3 did not enhance the osteogenic response.<br /

Gyroscopes based on nitrogen-vacancy centers in diamond

We propose solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (${\rm NV^-}$) centers in diamond. In one scheme, rotation of the nitrogen-vacancy symmetry axis will induce Berry phase shifts in the ${\rm NV^{-}}$ electronic ground-state coherences proportional to the solid angle subtended by the symmetry axis. We estimate sensitivity in the range of $5\times10^{-3} {\rm rad/s/\sqrt{Hz}}$ in a 1 ${\rm mm^3}$ sensor volume using a simple Ramsey sequence. Incorporating dynamical decoupling to suppress dipolar relaxation may yield sensitivity at the level of $10^{-5} {\rm rad/s/\sqrt{Hz}}$. With a modified Ramsey scheme, Berry phase shifts in the ${\rm ^{14}N}$ hyperfine sublevels would be employed. The projected sensitivity is in the range of $10^{-5} {\rm rad/s/\sqrt{Hz}}$, however the smaller gyromagnetic ratio reduces sensitivity to magnetic-field noise by several orders of magnitude. Reaching $10^{-5} {\rm rad/s/\sqrt{Hz}}$ would represent an order of magnitude improvement over other compact, solid-state gyroscope technologies.Comment: 3 figures, 5 page

Can Galactic Observations Be Explained by a Relativistic Gravity Theory?

We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression for the metric to order $(v/c)^2$. This allows us to compare the predictions of the theory with various experimental data: the Newtonian limit, light deflection and retardation, rotation of galaxies and gravitational lensing. Our general conclusion is that the possibility for any gravity theory to explain the behaviour of galaxies without dark matter is rather improbable.Comment: 12p, REVTeX 3.

Properties of galaxy dark matter halos from weak lensing

We present the results of a study of weak lensing by galaxies based on 45.5 deg$^2$ of $R_C$ band imaging data from the Red-Sequence Cluster Survey (RCS). We present the first weak lensing detection of the flattening of galaxy dark matter halos. We use a simple model in which the ellipticity of the halo is $f$ times the observed ellipticity of the lens. We find a best fit value of $f=0.77^{+0.18}_{-0.21}$, suggesting that the dark matter halos are somewhat rounder than the light distribution. The fact that we detect a significant flattening implies that the halos are well aligned with the light distribution. Given the average ellipticity of the lenses, this implies a halo ellipticity of $=0.33^{+0.07}_{-0.09}$, in fair agreement with results from numerical simulations of CDM. This result provides strong support for the existence of dark matter, as an isotropic lensing signal is excluded with 99.5% confidence. We also study the average mass profile around the lenses, using a maximum likelihood analysis. We consider two models for the halo mass profile: a truncated isothermal sphere (TIS) and an NFW profile. We adopt observationally motivated scaling relations between the lens luminosity and the velocity dispersion and the extent of the halo. The best fit NFW model yields a mass $M_{200}=(8.4\pm0.7\pm0.4)\times 10^{11} h^{-1} M_\odot$ and a scale radius $r_s=16.2^{+3.6}_{-2.9} h^{-1}$ kpc. This value for the scale radius is in excellent agreement with predictions from numerical simulations for a halo of this mass.Comment: Significantly revised version, accepted for publication in ApJ 11 pages, 6 figure

The formation of cosmic structure with modified Newtonian dynamics

I consider the growth of inhomogeneities in a low-density baryonic, vacuum energy-dominated universe in the context of modified Newtonian dynamics (MOND). I first write down a two-field Langrangian-based theory of MOND (non-relativistic), which embodies several assumptions such as constancy of the MOND acceleration parameter, association of a MOND force with peculiar accelerations only, and the deceleration of the Hubble flow as a background field which influences the dynamics of a finite size region. In the context of this theory, the equation for the evolution of spherically symmetric over-densities is non-linear and implies very rapid growth even in a low-density background, particularly at the epoch when the putative cosmological constant begins to dominate the Hubble expansion. Small comoving scales enter the MOND regime earlier than larger scales and therefore evolve to large over-densities sooner. Taking the initial COBE-normalized power spectrum provided by CMBFAST (Seljak & Zeldarriaga 1996), I find that the final power-spectrum resembles that of the standard LCDM universe and thus retains the empirical successes of that model.Comment: revised version includes a Lagrangian-based, non-relativistic theory of modified dynamics; conclusions are unchanged; accepted for publication (ApJ