782 research outputs found
On Relativistic Perturbations of Second and Higher Order
We present the results of a study of the gauge dependence of spacetime
perturbations. In particular, we consider gauge invariance in general, we give
a generating formula for gauge transformations to an arbitrary order n, and
explicit transformation rules at second order.Comment: 6 pages, latex, with special style included, Proceedings of the 12th
Italian Conference on General Relativity and Gravitational Physic
Relativistic second-order perturbations of the Einstein-de Sitter Universe
We consider the evolution of relativistic perturbations in the Einstein-de
Sitter cosmological model, including second-order effects. The perturbations
are considered in two different settings: the widely used synchronous gauge and
the Poisson (generalized longitudinal) one. Since, in general, perturbations
are gauge dependent, we start by considering gauge transformations at second
order. Next, we give the evolution of perturbations in the synchronous gauge,
taking into account both scalar and tensor modes in the initial conditions.
Using the second-order gauge transformation previously defined, we are then
able to transform these perturbations to the Poisson gauge. The most important
feature of second-order perturbation theory is mode-mixing, which here also
means, for instance, that primordial density perturbations act as a source for
gravitational waves, while primordial gravitational waves give rise to
second-order density fluctuations. Possible applications of our formalism range
from the study of the evolution of perturbations in the mildly non-linear
regime to the analysis of secondary anisotropies of the Cosmic Microwave
Background.Comment: Revised version with minor changes, accepted in The Physical Review
D; LaTeX file using RevTeX macros, 28 page
Lensing of ultra-high energy cosmic rays in turbulent magnetic fields
We consider the propagation of ultra high energy cosmic rays through
turbulent magnetic fields and study the transition between the regimes of
single and multiple images of point-like sources. The transition occurs at
energies around , where is the distance traversed by the
CR's with electric charge in the turbulent magnetic field of root mean
square strength and coherence length . We find that above only sources located in a fraction of a few % of the sky can reach large
amplifications of its principal image or start developing multiple images. New
images appear in pairs with huge magnifications, and they remain amplified over
a significant range of energies. At decreasing energies the fraction of the sky
in which sources can develop multiple images increases, reaching about 50% for
. The magnification peaks become however increasingly narrower and for
their integrated effect becomes less noticeable. If a uniform
magnetic field component is also present it would further narrow down the
peaks, shrinking the energy range in which they can be relevant. Below some kind of scintillation regime is reached, where many demagnified
images of a source are present but with overall total magnification of order
unity. We also search for lensing signatures in the AGASA data studying
two-dimensional correlations in angle and energy and find some interesting
hints.Comment: 30 pages, 16 figures, final version with minor change
Gravitational lensing as folds in the sky
We revisit the gravitational lensing phenomenon using a new visualization
technique. It consists in projecting the observers sky into the source plane,
what gives rise to a folded and stretched surface. This provides a clear
graphical tool to visualize some interesting well-known effects, such as the
development of multiple images of a source, the structure of the caustic
curves, the parity of the images and their magnification as a function of the
source position.Comment: 11 pages, 8 figure
CMB polarization from secondary vector and tensor modes
We consider a novel contribution to the polarization of the Cosmic Microwave
Background induced by vector and tensor modes generated by the non-linear
evolution of primordial scalar perturbations. Our calculation is based on
relativistic second-order perturbation theory and allows to estimate the
effects of these secondary modes on the polarization angular power-spectra. We
show that a non-vanishing B-mode polarization unavoidably arises from pure
scalar initial perturbations, thus limiting our ability to detect the signature
of primordial gravitational waves generated during inflation. This secondary
effect dominates over that of primordial tensors for an inflationary
tensor-to-scalar ratio . The magnitude of the effect is smaller than
the contamination produced by the conversion of polarization of type E into
type B, by weak gravitational lensing. However the lensing signal can be
cleaned, making the secondary modes discussed here the actual background
limiting the detection of small amplitude primordial gravitational waves.Comment: 14 pages, 3 figures, minor changes matching the version to be
published in Phys. Rev.
CMB anisotropy: deviations from Gaussianity due to non-linear gravity
Non-linear evolution of cosmological energy density fluctuations triggers
deviations from Gaussianity in the temperature distribution of the cosmic
microwave background. A method to estimate these deviations is proposed. N-body
simulations -- in a CDM cosmology -- are used to simulate the strongly
non-linear evolution of cosmological structures. It is proved that these
simulations can be combined with the potential approximation to calculate the
statistical moments of the CMB anisotropies produced by non-linear gravity.
Some of these moments are computed and the resulting values are different from
those corresponding to Gaussianity.Comment: 6 latex pages with mn.sty, 3 eps figures. Accepted in MNRA
A Three-Point Cosmic Ray Anisotropy Method
The two-point angular correlation function is a traditional method used to
search for deviations from expectations of isotropy. In this paper we develop
and explore a statistically descriptive three-point method with the intended
application being the search for deviations from isotropy in the highest energy
cosmic rays. We compare the sensitivity of a two-point method and a
"shape-strength" method for a variety of Monte-Carlo simulated anisotropic
signals. Studies are done with anisotropic source signals diluted by an
isotropic background. Type I and II errors for rejecting the hypothesis of
isotropic cosmic ray arrival directions are evaluated for four different event
sample sizes: 27, 40, 60 and 80 events, consistent with near term data
expectations from the Pierre Auger Observatory. In all cases the ability to
reject the isotropic hypothesis improves with event size and with the fraction
of anisotropic signal. While ~40 event data sets should be sufficient for
reliable identification of anisotropy in cases of rather extreme (highly
anisotropic) data, much larger data sets are suggested for reliable
identification of more subtle anisotropies. The shape-strength method
consistently performs better than the two point method and can be easily
adapted to an arbitrary experimental exposure on the celestial sphere.Comment: Fixed PDF erro
Decaying neutron propagation in the Galaxy and the Cosmic Ray anisotropy at 1 EeV
We study the cosmic ray arrival distribution expected from a source of
neutrons in the galactic center at energies around 1 EeV and compare it with
the anisotropy detected by AGASA and SUGAR. Besides the point-like signal in
the source direction produced by the direct neutrons, an extended signal due to
the protons produced in neutron decays is expected. This associated proton
signal also leads to an excess in the direction of the spiral arm. For
realistic models of the regular and random galactic magnetic fields, the
resulting anisotropy as a function of the energy is obtained. We find that for
the anisotropy to become sufficiently suppressed below E\sim 10^{17.9}eV, a
significant random magnetic field component is required, while on the other
hand, this also tends to increase the angular spread of the associated proton
signal and to reduce the excess in the spiral arm direction. The source
luminosity required in order that the right ascension anisotropy be 4% for the
AGASA angular exposure corresponds to a prediction for the point-like flux from
direct neutrons compatible with the flux detected by SUGAR. We also analyse the
distinguishing features predicted for a large statistics southern observatory.Comment: 14 pages, 6 figures, minor changes to match published versio
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