65,153 research outputs found
Hamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the
one-dimensional homogeneous potential, , where and
are continuously varying parameters. In the non-relativistic case, the
exact analytical solution is determined in terms of , and the total
energy . It is also shown that the non-linear equation of motion can be
linearized by constructing a hypergeometric differential equation for the
inverse problem . A variable transformation reducing the general problem
to that one of a particle subjected to a linear force is also established. For
any value of , it leads to a simple harmonic oscillator if , an
"anti-oscillator" if , or a free particle if E=0. However, such a
reduction is not possible in the relativistic case. For a bounded relativistic
motion, the first order correction to the period is determined for any value of
. For , it is found that the correction is just twice that one
deduced for the simple harmonic oscillator (), and does not depend on the
specific value of .Comment: 12 pages, Late
Ages and metallicities of star clusters: new calibrations and diagnostic diagrams from visible integrated spectra
We present homogeneous scales of ages and metallicities for star clusters
from very young objects, through intermediate-age ones up to the oldest known
clusters. All the selected clusters have integrated spectra in the visible
range, as well as reliable determinations of their ages and metallicities. From
these spectra equivalent widths (EWs) of KCaII, Gband(CH) and MgI metallic, and
Hdelta, Hgamma and Hbeta Balmer lines have been measured homogeneously. The
analysis of these EWs shows that the EW sums of the metallic and Balmer H
lines, separately, are good indicators of cluster age for objects younger than
10 Gyr, and that the former is also sensitive to cluster metallicity for ages
greater than 10 Gyr. We propose an iterative procedure for estimating cluster
ages by employing two new diagnostic diagrams and age calibrations based on the
above EW sums. For clusters older than 10 Gyr, we also provide a calibration to
derive their overall metal contents.Comment: 9 pages, 4 figures, accepted by A&
Is CDM an effective CCDM cosmology?
We show that a cosmology driven by gravitationally induced particle
production of all non-relativistic species existing in the present Universe
mimics exactly the observed flat accelerating CDM cosmology with just
one dynamical free parameter. This kind of scenario includes the creation cold
dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a
particular case and also provides a natural reduction of the dark sector since
the vacuum component is not needed to accelerate the Universe. The new cosmic
scenario is equivalent to CDM both at the background and perturbative
levels and the associated creation process is also in agreement with the
universality of the gravitational interaction and equivalence principle.
Implicitly, it also suggests that the present day astronomical observations
cannot be considered the ultimate proof of cosmic vacuum effects in the evolved
Universe because CDM may be only an effective cosmology.Comment: 6 pages, 2 figures, changes in the abstract, introduction, new
references and typo correction
Studying light propagation in a locally homogeneous universe through an extended Dyer-Roeder approach
Light is affected by local inhomogeneities in its propagation, which may
alter distances and so cosmological parameter estimation. In the era of
precision cosmology, the presence of inhomogeneities may induce systematic
errors if not properly accounted. In this vein, a new interpretation of the
conventional Dyer-Roeder (DR) approach by allowing light received from distant
sources to travel in regions denser than average is proposed. It is argued that
the existence of a distribution of small and moderate cosmic voids (or "black
regions") implies that its matter content was redistributed to the homogeneous
and clustered matter components with the former becoming denser than the cosmic
average in the absence of voids. Phenomenologically, this means that the DR
smoothness parameter (denoted here by ) can be greater than unity,
and, therefore, all previous analyses constraining it should be rediscussed
with a free upper limit. Accordingly, by performing a statistical analysis
involving 557 type Ia supernovae (SNe Ia) from Union2 compilation data in a
flat CDM model we obtain for the extended parameter,
(). The effects of are also
analyzed for generic CDM models and flat XCDM cosmologies. For both
models, we find that a value of greater than unity is able to
harmonize SNe Ia and cosmic microwave background observations thereby
alleviating the well-known tension between low and high redshift data. Finally,
a simple toy model based on the existence of cosmic voids is proposed in order
to justify why can be greater than unity as required by supernovae
data.Comment: 5 pages, 2 figures. Title modified, results unchanged. It matches
version published as a Brief Report in Phys. Rev.
On FRW Model in Conformal Teleparallel Gravity
In this paper we use the conformal teleparallel gravity to study an isotropic
and homogeneous Universe which is settled by the FRW metric. We solve the field
equations and we obtain the behavior of some cosmological parameters such as
scale factor, deceleration parameter and the energy density of the perfect
fluid which is the matter field of our model. The field equations, that we
called modified Friedmann equations, allow us to define a dark fluid, with dark
energy density and dark pressure, responsible for the acceleration in the
Universe.Comment: Accepted in EPJ
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