27,733 research outputs found
A Note on Commuting Diffeomorphisms on Surfaces
Let S be a closed surface with nonzero Euler characteristic. We prove the
existence of an open neighborhood V of the identity map of S in the
C^1-topology with the following property: if G is an abelian subgroup of
Diff^1(S) generated by any family of elements in V then the elements of G have
common fixed points. This result generalizes a similar result due to Bonatti
and announced in his paper "Diffeomorphismes commutants des surfaces et
stabilite des fibrations en tores".Comment: 16 page
Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model
We investigate the phase diagram of a spin- Ising model on a cubic
lattice, with competing interactions between nearest and next-nearest neighbors
along an axial direction, and fully connected spins on the sites of each
perpendicular layer. The problem is formulated in terms of a set of
noninteracting Ising chains in a position-dependent field. At low temperatures,
as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising
(ANNNI) model, there are many distinct spatially commensurate phases that
spring from a multiphase point of infinitely degenerate ground states. As
temperature increases, we confirm the existence of a branching mechanism
associated with the onset of higher-order commensurate phases. We check that
the ferromagnetic phase undergoes a first-order transition to the modulated
phases. Depending on a parameter of competition, the wave number of the striped
patterns locks in rational values, giving rise to a devil's staircase. We
numerically calculate the Hausdorff dimension associated with these
fractal structures, and show that increases with temperature but seems
to reach a limiting value smaller than .Comment: 17 pages, 6 figure
Reflection matrices for the vertex model
The graded reflection equation is investigated for the
vertex model. We have found four classes of diagonal
solutions and twelve classes of non-diagonal ones. The number of free
parameters for some solutions depends on the number of bosonic and fermionic
degrees of freedom considered.Comment: 30 page
Dynamics and Constraints of the Massive Gravitons Dark Matter Flat Cosmologies
We discuss the dynamics of the universe within the framework of Massive
Graviton Dark Matter scenario (MGCDM) in which gravitons are geometrically
treated as massive particles. In this modified gravity theory, the main effect
of the gravitons is to alter the density evolution of the cold dark matter
component in such a way that the Universe evolves to an accelerating expanding
regime, as presently observed. Tight constraints on the main cosmological
parameters of the MGCDM model are derived by performing a joint likelihood
analysis involving the recent supernovae type Ia data, the Cosmic Microwave
Background (CMB) shift parameter and the Baryonic Acoustic Oscillations (BAOs)
as traced by the Sloan Digital Sky Survey (SDSS) red luminous galaxies. The
linear evolution of small density fluctuations is also analysed in detail. It
is found that the growth factor of the MGCDM model is slightly different
() from the one provided by the conventional flat CDM
cosmology. The growth rate of clustering predicted by MGCDM and CDM
models are confronted to the observations and the corresponding best fit values
of the growth index () are also determined. By using the expectations
of realistic future X-ray and Sunyaev-Zeldovich cluster surveys we derive the
dark-matter halo mass function and the corresponding redshift distribution of
cluster-size halos for the MGCDM model. Finally, we also show that the Hubble
flow differences between the MGCDM and the CDM models provide a halo
redshift distribution departing significantly from the ones predicted by other
DE models. These results suggest that the MGCDM model can observationally be
distinguished from CDM and also from a large number of dark energy
models recently proposed in the literature.Comment: Accepted for publication in Physical Review D (12 pages, 4 figures
New Cosmic Accelerating Scenario without Dark Energy
We propose an alternative, nonsingular, cosmic scenario based on
gravitationally induced particle production. The model is an attempt to evade
the coincidence and cosmological constant problems of the standard model
(CDM) and also to connect the early and late time accelerating stages
of the Universe. Our space-time emerges from a pure initial de Sitter stage
thereby providing a natural solution to the horizon problem. Subsequently, due
to an instability provoked by the production of massless particles, the
Universe evolves smoothly to the standard radiation dominated era thereby
ending the production of radiation as required by the conformal invariance.
Next, the radiation becomes sub-dominant with the Universe entering in the cold
dark matter dominated era. Finally, the negative pressure associated with the
creation of cold dark matter (CCDM model) particles accelerates the expansion
and drives the Universe to a final de Sitter stage. The late time cosmic
expansion history of the CCDM model is exactly like in the standard
CDM model, however, there is no dark energy. This complete scenario is
fully determined by two extreme energy densities, or equivalently, the
associated de Sitter Hubble scales connected by , a result that has no correlation with the cosmological constant
problem. We also study the linear growth of matter perturbations at the final
accelerating stage. It is found that the CCDM growth index can be written as a
function of the growth index, . In this
framework, we also compare the observed growth rate of clustering with that
predicted by the current CCDM model. Performing a statistical test
we show that the CCDM model provides growth rates that match sufficiently well
with the observed growth rate of structure.Comment: 12 pages, 3 figures, accepted for publication by Phys. Rev. D. (final
version, some references have corrected). arXiv admin note: substantial text
overlap with arXiv:1106.193
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