9,190 research outputs found
Hyperbolic-parabolic deformations of rational maps
We develop a Thurston-like theory to characterize geometrically finite
rational maps, then apply it to study pinching and plumbing deformations of
rational maps. We show that in certain conditions the pinching path converges
uniformly and the quasiconformal conjugacy converges uniformly to a
semi-conjugacy from the original map to the limit. Conversely, every
geometrically finite rational map with parabolic points is the landing point of
a pinching path for any prescribed plumbing combinatorics.Comment: 78 pages, 6 figure
Comparing holographic dark energy models with statefinder
We apply the statefinder diagnostic to the holographic dark energy models,
including the original holographic dark energy (HDE) model, the new holographic
dark energy model, the new agegraphic dark energy (NADE) model, and the Ricci
dark energy model. In the low-redshift region the holographic dark energy
models are degenerate with each other and with the CDM model in the
and evolutions. In particular, the HDE model is highly degenerate
with the CDM model, and in the HDE model the cases with different
parameter values are also in strong degeneracy. Since the observational data
are mainly within the low-redshift region, it is very important to break this
low-redshift degeneracy in the and diagnostics by using some
quantities with higher order derivatives of the scale factor. It is shown that
the statefinder diagnostic is very useful in breaking the low-redshift
degeneracies. By employing the statefinder diagnostic the holographic dark
energy models can be differentiated efficiently in the low-redshift region. The
degeneracy between the holographic dark energy models and the CDM
model can also be broken by this method. Especially for the HDE model, all the
previous strong degeneracies appearing in the and diagnostics are
broken effectively. But for the NADE model, the degeneracy between the cases
with different parameter values cannot be broken, even though the statefinder
diagnostic is used. A direct comparison of the holographic dark energy models
in the -- plane is also made, in which the separations between the models
(including the CDM model) can be directly measured in the light of the
current values of the models.Comment: 8 pages, 8 figures; accepted by European Physical Journal C; matching
the publication versio
No evidence for the evolution of mass density power-law index from strong gravitational lensing observation
In this paper, we consider the singular isothermal sphere lensing model that
has a spherically symmetric power-law mass distribution . We investigate whether the mass density power-law index
is cosmologically evolutionary by using the strong gravitational lensing (SGL)
observation, in combination with other cosmological observations. We also check
whether the constraint result of is affected by the cosmological
model, by considering several simple dynamical dark energy models. We find that
the constraint on is mainly decided by the SGL observation and
independent of the cosmological model, and we find no evidence for the
evolution of from the SGL observation.Comment: 7 pages, 3 figure
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