1,424 research outputs found
Poincar\'e's polyhedron theorem for cocompact groups in dimension 4
We prove a version of Poincar\'e's polyhedron theorem whose requirements are
as local as possible. New techniques such as the use of discrete groupoids of
isometries are introduced. The theorem may have a wide range of applications
and can be generalized to the case of higher dimension and other geometric
structures. It is planned as a first step in a program of constructing compact
-surfaces of general type satisfying .Comment: 15 pages, 1 figure, 9 references. Introduction revised. Example 3.16
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Modified gravity models and the central cusp of dark matter haloes in galaxies
The N-body dark matter (DM) simulations point that DM density profiles, e.g. the Navarro Frenk White (NFW) halo, should be cuspy in its centre, but observations disfavour this kind of DM profile. Here we consider whether the observed rotation curves close to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, Modified Newtonian Dynamics (MOND) and a more recent approach renormalization group effects in general relativity (RGGR). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches. By analysing 62 galaxies from five samples, we find that (i) there is a radius, given by half the disc scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; (ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have, respectively, two and one more free parameters than MOND)
Renormalization Group approach to Gravity: the running of G and L inside galaxies and additional details on the elliptical NGC 4494
We explore the phenomenology of nontrivial quantum effects on low-energy
gravity. These effects come from the running of the gravitational coupling
parameter G and the cosmological constant L in the Einstein-Hilbert action, as
induced by the Renormalization Group (RG). The Renormalization Group corrected
General Relativity (RGGR model) is used to parametrize these quantum effects,
and it is assumed that the dominant dark matter-like effects inside galaxies is
due to these nontrivial RG effects. Here we present additional details on the
RGGR model application, in particular on the Poisson equation extension that
defines the effective potential, also we re-analyse the ordinary elliptical
galaxy NGC 4494 using a slightly different model for its baryonic contribution,
and explicit solutions are presented for the running of G and L. The values of
the NGC 4494 parameters as shown here have a better agreement with the general
RGGR picture for galaxies, and suggest a larger radial anisotropy than the
previously published result.Comment: 9 pages, 2 figs. Based on a talk presented at the VIII International
Workshop on the Dark Side of the Universe, June 10-15, 2012, Buzios, RJ,
Brazil. v2: typos removed, matches published versio
Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation
We discuss solutions of Vlasov-Einstein equation for collisionless dark
matter particles in the context of a flat Friedmann universe. We show that,
after decoupling from the primordial plasma, the dark matter phase-space
density indicator Q remains constant during the expansion of the universe,
prior to structure formation. This well known result is valid for
non-relativistic particles and is not "observer dependent" as in solutions
derived from the Vlasov-Poisson system. In the linear regime, the inclusion of
velocity dispersion effects permits to define a physical Jeans length for
collisionless matter as function of the primordial phase-space density
indicator: \lambda_J = (5\pi/G)^(1/2)Q^(-1/3)\rho_dm^(-1/6). The comoving Jeans
wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the
comoving wavenumber due to free-streaming, contributing to the cut-off of the
density fluctuation power spectrum at the lowest scales. We discuss the
physical differences between these two scales. For dark matter particles of
mass equal to 200 GeV, the derived Jeans mass is 4.3 x 10^(-6) solar masses.Comment: 18 pages, 2 figures. Accepted for publication in JCA
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