Refining MOND interpolating function and TeVeS Lagrangian

The phenomena customly called Dark Matter or Modified Newtonian Dynamics (MOND) have been argued by Bekenstein (2004) to be the consequences of a covariant scalar field, controlled by a free function (related to the MOND interpolating function) in its Lagrangian density. In the context of this relativistic MOND theory (TeVeS), we examine critically the interpolating function in the transition zone between weak and strong gravity. Bekenstein's toy model produces too gradually varying functions and fits rotation curves less well than the standard MOND interpolating function. However, the latter varies too sharply and implies an implausible external field effect (EFE). These constraints on opposite sides have not yet excluded TeVeS, but made the zone of acceptable interpolating functions narrower. An acceptable "toy" Lagrangian density function with simple analytical properties is singled out for future studies of TeVeS in galaxies. We also suggest how to extend the model to solar system dynamics and cosmology, and compare with strong lensing data (see also astro-ph/0509590).Comment: accepted for publication in ApJ Letter

Self-consistent models of triaxial galaxies in MOND gravity

The Bekenstein-Milgrom gravity theory with a modified Poisson equation is tested here for the existence of triaxial equilibrium solutions. Using the non-negative least square method, we show that self-consistent triaxial galaxies exist for baryonic models with a mild density cusp $\rho \sim {\Sigma \over r}$. Self-consistency is achieved for a wide range of central concentrations, $\Sigma \sim 10-1000\mathrm{M_{\odot}pc^{-2}}$, representing low-to-high surface brightness galaxies. Our results demonstrate for the first time that the orbit superposition technique is fruitful for constructing galaxy models beyond Newtonian gravity, and triaxial cuspy galaxies might exist without the help of Cold dark Matter.Comment: 19 pages, 1 table, 7 figures, Accepted for publication in Ap

Short-coherence length superconductivity in the Attractive Hubbard Model in three dimensions

We study the normal state and the superconducting transition in the Attractive Hubbard Model in three dimensions, using self-consistent diagrammatics. Our results for the self-consistent $T$-matrix approximation are consistent with 3D-XY power-law critical scaling and finite-size scaling. This is in contrast to the exponential 2D-XY scaling the method was able to capture in our previous 2D calculation. We find the 3D transition temperature at quarter-filling and $U=-4t$ to be $T_c=0.207t$. The 3D critical regime is much narrower than in 2D and the ratio of the mean-field transition to $T_c$ is about 5 times smaller than in 2D. We also find that, for the parameters we consider, the pseudogap regime in 3D (as in 2D) coincides with the critical scaling regime.Comment: 4 pages, 5 figure

Weak Lensing of Galaxy Clusters in MOND

We study weak gravitational lensing of galaxy clusters in terms of the MOND (MOdified Newtonian Dynamics) theory. We calculate shears and convergences of background galaxies for three clusters (A1689, CL0024+1654, CL1358+6245) and the mean profile of 42 SDSS (Sloan Digital Sky Survey) clusters and compare them with observational data. The mass profile is modeled as a sum of X-ray gas, galaxies and dark halo. For the shear as a function of the angular radius, MOND predicts a shallower slope than the data irrespective of the critical acceleration parameter $g_0$. The dark halo is necessary to explain the data for any $g_0$ and for three interpolation functions. If the dark halo is composed of massive neutrinos, its mass should be heavier than 2 eV. However the constraint still depends on the dark halo model and there are systematic uncertainties, and hence the more careful study is necessary to put a stringent constraint.Comment: 12 pages, 7 figures, references added, minor changes, accepted for publication in Ap