Gravitational instabilities and faster evolving density perturbations

The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes. In addition to the usual modes, an infinite number of new growing modes are contained in the solutions for pressureless open and closed universes. In the nonlinear regime, we obtain the leading growing modes in closed forms for a flat universe and also, in the limits of small and large times, for an open universe.Comment: latex, 17 pages; electronic address for programs correcte

Decay amplitudes in two-dimensional QCD

Decay amplitudes for mesons in two-dimensional QCD are discussed. We show that in spite of an infinite number of conserved charges, particle production is not entirely suppressed. This phenomenon is explained in terms of quantum corrections to the combined algebra of higher-conserved and spectrum-generating currents. We predict the qualitative form of particle production probabilities and verify that they are in agreement with numerical data. We also discuss four-dimensional self-dual Yang-Mills theory in the light of our results.Comment: We discuss in more detail the background material and elaborate on the consequences of the new results. New equations and text are added and the figures are efficiently regenerated by a fortran program, latex file, 13 pages, 4 figures in encapsulated postscript files, uses epsf. minor changes, version to appear in Physical Review

Higher-loop anomalies in chiral gravities

The one-loop anomalies for chiral $W_{3}$ gravity are derived using the Fujikawa regularisation method. The expected two-loop anomalies are then obtained by imposing the Wess-Zumino consistency conditions on the one-loop results. The anomalies found in this way agree with those already known from explicit Feynman diagram calculations. We then directly verify that the order $\hbar^2$ non-local BRST Ward identity anomalies, arising from the ``dressing'' of the one-loop results, satisfy Lam's theorem. It is also shown that in a rigorous calculation of $Q^2$ anomaly for the BRST charge, one recovers both the non-local as well as the local anomalies. We further verify that, in chiral gravities, the non-local anomalies in the BRST Ward identity can be obtained by the application of the anomalous operator $Q^2$, calculated using operator products, to an appropriately defined gauge fermion. Finally, we give arguments to show why this relation should hold generally in reparametrisation-invariant theories.Comment: 21 pages, latex, 12 figures as uuencoded postscript. To appear in Nucl. Phys.

Dark matter caustics and the enhancement of self-annihilation flux

Cold dark matter haloes are populated by caustics, which are yet to be resolved in N-body simulations or observed in the Universe. Secondary infall model provides a paradigm for the study of caustics in "typical" haloes assuming that they have had no major mergers and have grown only by smooth accretion. This is a particular characteristic of the smallest dark matter haloes of about 10^{-5} Mo, which although "atypical" contain no substructures and could have survived until now with no major mergers. Thus using this model as the first guidline, we evaluate the neutralino self-annihilation flux for these haloes. Our results show that caustics could leave a distinct sawteeth signature on the differential and cumulative fluxes coming from the outer regions of these haloes. The total annihilation signal from the regions away from the centre can be boosted by about forty percents.Comment: To appear in JCAP, 4 pages, 3 figure

A single-merger scenario for the formation of the giant stream and the warp of M31

We propose that the accretion of a dwarf spheroidal galaxy provides a common origin for the giant southern stream and the warp of M31. We run about 40 full N-body simulations with live M31, infalling galaxies with varying masses and density profiles, and cosmologically-plausible initial orbital parameters. Excellent agreement with a full range of observational data is obtained for a model in which a dark-matter-rich dwarf spheroidal, whose trajectory lies on the thin plane of corotating satellites of M31, is accreted from its turnaround radius of about 200 kpcs into M31 at approximately 3 Gyrs ago. The satellite is disrupted as it orbits in the potential well of the galaxy and forms the giant stream and in return heats and warps the disk of M31. We show that our cosmologically-motivated model is favoured by the kinematic data over the phenomenological models in which the satellite starts its infall from a close distance of M31. Our model predicts that the remnant of the disrupted satellite resides in the region of the North-Eastern shelf of M31. The results here suggest that the surviving satellites of M31 that orbit on the same thin plane, as the disrupted satellite once did, could have all been accreted from an intergalactic filament.Comment: 18 pages, 22 figures, 3 table

The Monge-Amp\`ere-Kantorovich approach to reconstruction in cosmology

Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that transfers fluid elements in a way unaffected by any pressure or elasticity (the polar decomposition of Y. Brenier). The Euler equation describes a system whose kinematics is dominated by the incompressible rearrangement. The opposite limit, in which the incompressible component is negligible, corresponds to the Zel'dovich approximation, a model of motion of self-gravitating fluid in cosmology. We present a method of approximate reconstruction of the large-scale proper motions of matter in the Universe from the present-day mass density field. The method is based on recovering the corresponding gradient transfer map. We discuss its algorithmics, tests of the method against mock cosmological catalogues, and its application to observational data, which result in tight constraints on the mean mass density Omega_m and age of the Universe.Comment: 6 pages, 2 figures; based on an invited lecture at the conference "Euler's Equations: 250 Years On" (see http://www.obs-nice.fr/etc7/EE250/); to be published in a special issue of Physica D containing the proceedings of that conferenc

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant

The existence of critical points for the peculiar velocity field is a natural feature of the correlated vector field. These points appear at the junctions of velocity domains with different orientations of their averaged velocity vectors. Since peculiar velocities are the important cause of the scatter in the Hubble expansion rate, we propose that a more precise determination of the Hubble constant can be made by restricting analysis to a subsample of observational data containing only the zones around the critical points of the peculiar velocity field, associated with voids and saddle points. On large-scales the critical points, where the first derivative of the gravitational potential vanishes, can easily be identified using the density field and classified by the behavior of the Hessian of the gravitational potential. We use high-resolution N-body simulations to show that these regions are stable in time and hence are excellent tracers of the initial conditions. Furthermore, we show that the variance of the Hubble flow can be substantially minimized by restricting observations to the subsample of such regions of vanishing velocity instead of aiming at increasing the statistics by averaging indiscriminately using the full data sets, as is the common approach.Comment: 17 pages, 6 figures and 2 tables, minor modifications after receiving several useful comment