61,170 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
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 Lorentz violation in scattering at finite temperature
Small violation of Lorentz and CPT symmetries may emerge in models unifying
gravity with other forces of nature. An extension of the standard model with
all possible terms that violate Lorentz and CPT symmetries are included. Here a
CPT-even non-minimal coupling term is added to the covariant derivative. This
leads to a new interaction term that breaks the Lorentz symmetry. Our main
objective is to calculate the cross section for the
scattering in order to
investigate any violation of Lorentz and/or CPT symmetry at finite temperature.
Thermo Field Dynamics formalism is used to consider finite temperature effects.Comment: 12 pages, 1 figure, accepted for publication in PL
Probing the Cosmological Principle in the counts of radio galaxies at different frequencies
According to the Cosmological Principle, the matter distribution on very
large scales should have a kinematic dipole that is aligned with that of the
CMB. We determine the dipole anisotropy in the number counts of two all-sky
surveys of radio galaxies. For the first time, this analysis is presented for
the TGSS survey, allowing us to check consistency of the radio dipole at low
and high frequencies by comparing the results with the well-known NVSS survey.
We match the flux thresholds of the catalogues, with flux limits chosen to
minimise systematics, and adopt a strict masking scheme. We find dipole
directions that are in good agreement with each other and with the CMB dipole.
In order to compare the amplitude of the dipoles with theoretical predictions,
we produce sets of lognormal realisations. Our realisations include the
theoretical kinematic dipole, galaxy clustering, Poisson noise, simulated
redshift distributions which fit the NVSS and TGSS source counts, and errors in
flux calibration. The measured dipole for NVSS is times larger than
predicted by the mock data. For TGSS, the dipole is almost times
larger than predicted, even after checking for completeness and taking account
of errors in source fluxes and in flux calibration. Further work is required to
understand the nature of the systematics that are the likely cause of the
anomalously large TGSS dipole amplitude.Comment: 13 pages, 8 figures, 2 tables; Significant improvements. Version
accepted by JCA
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
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