1,520 research outputs found
General solution for scalar perturbations in bouncing cosmologies
Bouncing cosmologies, suggested by String/M-theory, may provide an
alternative to standard inflation to account for the origin of inhomogeneities
in our universe. The fundamental question regards the correct way to evolve the
scalar perturbations through the bounce. In this work, we determine the
evolution of perturbations and the final spectrum for an arbitrary (spatially
flat) bouncing cosmology, with the only assumption that the bounce is governed
by a single physical scale. In particular, we find that the spectrum of the
pre-bounce growing mode of the Bardeen potential (which is scale-invariant in
some limit, and thus compatible with observations) survives unaltered in the
post-bounce only if the comoving pressure perturbation is directly proportional
to the Bardeen potential rather than its Laplacian, as for any known form of
ordinary matter. If some new physics acting at the bounce justifies such
relation, then bouncing cosmologies are entitled to become a real viable
alternative for the generation of the observed inhomogeneities. Our treatment
also includes some class of models with extra-dimensions, whereas we show that
bounces induced by positive spatial curvature are structurally different from
all bounces in spatially flat universes, requiring a distinct analysis.Comment: 24 pages, 2 figure
Caustics in special multiple lenses
Despite its mathematical complexity, the multiple gravitational lens can be
studied in detail in every situation where a perturbative approach is possible.
In this paper, we examine the caustics of a system with a lens very far from
the others with respect to their Einstein radii, and a system where mutual
distances between lenses are small compared to the Einstein radius of the total
mass. Finally we review the case of a planetary system adding some new
information (area of caustics, duality and higher order terms).Comment: 11 pages, 7 figures, submitted to A &
A solution to the anisotropy problem in bouncing cosmologies
Bouncing cosmologies are often proposed as alternatives to standard inflation
for the explanation of the homogeneity and flatness of the universe. In such
scenarios, the present cosmological expansion is preceded by a contraction
phase. However, during the contraction, in general the anisotropy of the
universe grows and eventually leads to a chaotic mixmaster behavior. This would
either be hard to reconcile with observations or even lead to a singularity
instead of the bounce. In order to preserve a smooth and isotropic bounce, the
source for the contraction must have a super-stiff equation of state with
. In this letter we propose a new mechanism to solve the anisotropy
problem for any low-energy value of by arguing that high energy physics
leads to a modification of the equation of state, with the introduction of
non-linear terms. In such a scenario, the anisotropy is strongly suppressed
during the high energy phase, allowing for a graceful isotropic bounce, even
when the low-energy value of is smaller than unity.Comment: 9 pages, accepted for publication in JCA
Caustics of binary gravitational lenses: from galactic haloes to exotic matter
We investigate the caustic topologies for binary gravitational lenses made up
of two objects whose gravitational potential declines as . With
this corresponds to power-law dust distributions like the singular isothermal
sphere. The regime can be obtained with some violations of the energy
conditions, one famous example being the Ellis wormhole. Gravitational lensing
provides a natural arena to distinguish and identify such exotic objects in our
Universe. We find that there are still three topologies for caustics as in the
standard Schwarzschild binary lens, with the main novelty coming from the
secondary caustics of the close topology, which become huge at higher .
After drawing caustics by numerical methods, we derive a large amount of
analytical formulae in all limits that are useful to provide deeper insight in
the mathematics of the problem. Our study is useful to better understand the
phenomenology of galaxy lensing in clusters as well as the distinct signatures
of exotic matter in complex systems.Comment: 28 pages, 19 figures, focus expanded to galactic haloe
Scalar perturbations in regular two-component bouncing cosmologies
We consider a two-component regular cosmology bouncing from contraction to
expansion, where, in order to include both scalar fields and perfect fluids as
particular cases, the dominant component is allowed to have an intrinsic
isocurvature mode. We show that the spectrum of the growing mode of the Bardeen
potential in the pre-bounce is never transferred to the dominant mode of the
post-bounce. The latter acquires at most a dominant isocurvature component,
depending on the relative properties of the two fluids. Our results imply that
several claims in the literature need substantial revision.Comment: 10 pages, 1 figur
Regular two-component bouncing cosmologies and perturbations therein
We present a full investigation of scalar perturbations in a rather generic
model for a regular bouncing universe, where the bounce is triggered by an
effective perfect fluid with negative energy density. Long before and after the
bounce the universe is dominated by a source with positive energy density,
which may be a perfect fluid, a scalar field, or any other source with an
intrinsic isocurvature perturbation. Within this framework, we present an
analytical method to accurately estimate the spectrum of large-scale scalar
perturbations until their reentry, long after the bounce. We also propose a
simple way to identify non-singular gauge-invariant variables through the
bounce and present the results of extensive numerical tests in several possible
realizations of the scenario. In no case do we find that the spectrum of the
pre-bounce growing mode of the Bardeen potential can be transferred to a
post-bounce constant mode.Comment: 19 pages, 9 figure
Gravitational Lensing of stars in the central arcsecond of our Galaxy
In the neighborhood of Sgr A*, several stars (S2, S12, S14, S1, S8, S13)
enjoy an accurate determination of their orbital parameters. General Relativity
predicts that the central black hole acts as a gravitational lens on these
stars, generating a secondary image and two infinite series of relativistic
images. For each of these six stars, we calculate the light curves for the
secondary and the first two relativistic images, in the Schwarzschild black
hole hypothesis, throughout their orbital periods. The curves are peaked around
the periapse epoch, but two subpeaks may arise in nearly edge-on orbits, when
the source is behind or in front of Sgr A*. We show that for most of these
stars the secondary image should be observable during its brightness peak. In
particular, S14 is the best candidate, since its secondary image reaches K=23.3
with an angular separation of 0.125 mas from the apparent horizon of the
central black hole. The detection of such images by future instruments could
represent the first observation of gravitational lensing beyond the weak field
approximation.Comment: 28 pages, 9 figures, in press on Ap
Observing gravitational lensing effects by Sgr A* with GRAVITY
The massive black hole at the Galactic center Sgr A* is surrounded by a
cluster of stars orbiting around it. Light from these stars is bent by the
gravitational field of the black hole, giving rise to several phenomena:
astrometric displacement of the primary image, the creation of a secondary
image that may shift the centroid of Sgr A*, magnification effects on both
images. The near-to-come second generation VLTI instrument GRAVITY will perform
observations in the Near Infrared of the Galactic Center at unprecedented
resolution, opening the possibility of observing such effects. Here we
investigate the observability limits for GRAVITY of gravitational lensing
effects on the S-stars in the parameter space [DLS,gamma,K], where DLS is the
distance between the lens and the source, gamma is the alignment angle of the
source, and K is the source apparent magnitude in the K-band. The easiest
effect to be observed in the next years is the astrometric displacement of
primary images. In particular the shift of the star S17 from its Keplerian
orbit will be detected as soon as GRAVITY becomes operative. For exceptional
configurations it will be possible to detect effects related to the spin of the
black hole or Post-Newtonian orders in the deflection.Comment: 29 pages, 9 figures, in press on Ap
Time Delay in Black Hole Gravitational Lensing as a Distance Estimator
We calculate the time delay between different relativistic images formed by
black hole gravitational lensing in the strong field limit. For spherically
symmetric black holes, it turns out that the time delay between the first two
images is proportional to the minimum impact angle. Their ratio gives a very
interesting and precise measure of the distance of the black hole. Moreover,
using also the separation between the images and their luminosity ratio, it is
possible to extract the mass of the black hole. The time delay for the black
hole at the center of our Galaxy is just few minutes, but for supermassive
black holes with M=10^8 - 10^9 solar masses in the neighbourhood of the Local
Group the time delay amounts to few days, thus being measurable with a good
accuracy.Comment: 8 pages, 3 figure
Relativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit
The shapes of relativistic iron lines observed in spectra of candidate black
holes carry the signatures of the strong gravitational fields in which the
accretion disks lie. These lines result from the sum of the contributions of
all images of the disk created by gravitational lensing, with the direct and
first-order images largely dominating the overall shapes. Higher order images
created by photons tightly winding around the black holes are often neglected
in the modeling of these lines, since they require a substantially higher
computational effort. With the help of the strong deflection limit, we present
the most accurate semi-analytical calculation of these higher order
contributions to the iron lines for Schwarzschild black holes. We show that two
regimes exist depending on the inclination of the disk with respect to the line
of sight. Many useful analytical formulae can be also derived in this
framework.Comment: 23 pages, 13 figure
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