2,270 research outputs found
On Shear-Free perturbations of FLRW Universes
A surprising exact result for the Einstein Field Equations is that if
pressure-free matter is moving in a shear-free way, then it must be either
expansion-free or rotation-free. It has been suggested this result is also true
for any barotropic perfect fluid, but a proof has remained elusive. We consider
the case of barotropic perfect fluid solutions linearized about a
Robertson-Walker geometry, and prove that the result remains true except for
the case of a specific highly non-linear equation of state. We argue that this
equation of state is non-physical, and hence the result is true in the
linearized case for all physically realistic barotropic perfect fluids. This
result, which is not true in Newtonian cosmology, demonstrates that the
linearized solutions, believed to result in standard local Newtonian theory, do
not always give the usual behaviour of Newtonian solutions
Constraints on Inflationary Solutions in the Presence of Shear and Bulk Viscosity
Inflationary models and their claim to solve many of the outstanding problems
in cosmology have been the subject of a great deal of debate over the last few
years. A major sticking point has been the lack of both good observational and
theoretical arguments to single out one particular model out of the many that
solve these problems. Here we examine the degree of restrictiveness on the
dynamical relationship between the cosmological scale factor and the inflation
driving self-interaction potential of a minimally coupled scalar field, imposed
by the condition that the scalar field is required to be real during a
classical regime (the reality condition). We systema\-tically look at the
effects of this constraint on many of the inflationary models found in the
literature within the FLRW framework, and also look at what happens when
physically motivated perturbations such as shear and bulk viscosity are
introduced. We find that in many cases, either the models are totally excluded
or the reality condition gives rise to constraints on the scale factor and on
the various parameters of the model.Comment: 21 pages, LaTe
Weak lensing B-modes on all scales as a probe of local isotropy
This article derives a multipolar hierarchy for the propagation of the
weak-lensing shear and convergence in a general spacetime. The origin of
B-modes, in particular on large angular scales, is related to the local
isotropy of space. Known results assuming a Friedmann-Lema\^itre background are
naturally recovered. The example of a Bianchi I spacetime illustrates our
formalism and its implications for future observations are stressed.Comment: 10 pages, 2 figures. Replaced to match published versio
Cosmic Electromagnetic Fields due to Perturbations in the Gravitational Field
We use non-linear gauge-invariant perturbation theory to study the
interaction of an inflation produced seed magnetic field with density and
gravitational wave perturbations in an almost
Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We compare the effects
of this coupling under the assumptions of poor conductivity, infinite
conductivity and the case where the electric field is sourced via the coupling
of velocity perturbations to the seed field in the ideal magnetohydrodynamic
(MHD) regime, thus generalizing, improving on and correcting previous results.
We solve our equations for long wavelength limits and numerically integrate the
resulting equations to generate power spectra for the electromagnetic field
variables, showing where the modes cross the horizon. We find that the rotation
of the electric field dominates the power spectrum on small scales, in
agreement with previous arguments.Comment: 16 pages, 3 figures, published in PR
A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity
We present a framework for the study of lensing in spherically symmetric
spacetimes within the context of f(R) gravity. Equations for the propagation of
null geodesics, together with an expression for the bending angle are derived
for any f(R) theory and then applied to an exact spherically symmetric solution
of R^n gravity. We find that for this case more bending is expected for R^n
gravity theories in comparison to GR and is dependent on the value of n and the
value of distance of closest approach of the incident null geodesic.Comment: 9 page
The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
We investigate whether or not an Einstein Static universe is a solution to
the cosmological equations in gravity. It is found that only one class
of theories admits an Einstein Static model, and that this class is
neutrally stable with respect to vector and tensor perturbations for all
equations of state on all scales. Scalar perturbations are only stable on all
scales if the matter fluid equation of state satisfies
. This result is remarkably similar to
the GR case, where it was found that the Einstein Static model is stable for
.Comment: Minor changes, To appear in PR
A fully covariant description of CMB anisotropies
Starting from the exact non-linear description of matter and radiation, a
fully covariant and gauge-invariant formula for the observed temperature
anisotropy of the cosmic microwave background (CBR) radiation, expressed in
terms of the electric () and magnetic () parts of the Weyl
tensor, is obtained by integrating photon geodesics from last scattering to the
point of observation today. This improves and extends earlier work by Russ et
al where a similar formula was obtained by taking first order variations of the
redshift. In the case of scalar (density) perturbations, is related to
the harmonic components of the gravitational potential and the usual
dominant Sachs-Wolfe contribution to the
temperature anisotropy is recovered, together with contributions due to the
time variation of the potential (Rees-Sciama effect), entropy and velocity
perturbations at last scattering and a pressure suppression term important in
low density universes. We also explicitly demonstrate the validity of assuming
that the perturbations are adiabatic at decoupling and show that if the surface
of last scattering is correctly placed and the background universe model is
taken to be a flat dust dominated Friedmann-Robertson-Walker model (FRW), then
the large scale temperature anisotropy can be interpreted as being due to the
motion of the matter relative to the surface of constant temperature which
defines the surface of last scattering on those scales.Comment: 18 pages LaTeX, 1 figure. Submitted to Classical and Quantum Gravity.
Also available at http://shiva.mth.uct.ac.za/preprints/9705.htm
Shear dynamics in Bianchi I cosmologies with R^n-gravity
We give the equations governing the shear evolution in Bianchi spacetimes for
general f(R)-theories of gravity. We consider the case of R^n-gravity and
perform a detailed analysis of the dynamics in Bianchi I cosmologies which
exhibit local rotational symmetry. We find exact solutions and study their
behaviour and stability in terms of the values of the parameter n. In
particular, we found a set of cosmic histories in which the universe is
initially isotropic, then develops shear anisotropies which approaches a
constant value.Comment: 25 pages LaTeX, 6 figures. Revised to match the final version
accepted for publication in CQ
Hubble flow variance and the cosmic rest frame
We characterize the radial and angular variance of the Hubble flow in the
COMPOSITE sample of 4534 galaxies, on scales in which much of the flow is in
the nonlinear regime. With no cosmological assumptions other than the existence
of a suitably averaged linear Hubble law, we find with decisive Bayesian
evidence (ln B >> 5) that the Hubble constant averaged in independent spherical
radial shells is closer to its asymptotic value when referred to the rest frame
of the Local Group, rather than the standard rest frame of the Cosmic Microwave
Background. An exception occurs for radial shells in the range 40/h-60/h Mpc.
Angular averages reveal a dipole structure in the Hubble flow, whose amplitude
changes markedly over the range 32/h-62/h Mpc. Whereas the LG frame dipole is
initially constant and then decreases significantly, the CMB frame dipole
initially decreases but then increases. The map of angular Hubble flow
variation in the LG rest frame is found to coincide with that of the residual
CMB temperature dipole, with correlation coefficient -0.92. These results are
difficult to reconcile with the standard kinematic interpretation of the motion
of the Local Group in response to the clustering dipole, but are consistent
with a foreground non-kinematic anisotropy in the distance-redshift relation of
0.5% on scales up to 65/h Mpc. Effectively, the differential expansion of space
produced by nearby nonlinear structures of local voids and denser walls and
filaments cannot be reduced to a local boost. This hypothesis suggests a
reinterpretation of bulk flows, which may potentially impact on calibration of
supernovae distances, anomalies associated with large angles in the CMB
anisotropy spectrum, and the dark flow inferred from the kinematic
Sunyaev-Zel'dovich effect. It is consistent with recent studies that find
evidence for a non-kinematic dipole in the distribution of distant radio
sources.Comment: 37 pages, 9 tables, 13 figures; v2 adds extensive new analysis
(including additional subsections, tables, figures); v3 adds a Monte Carlo
analysis (with additional table, figure) which further tightens the
statistical robustness of the dipole results; v4 adds further clarifications,
small corrections, references and discussion of Planck satellite results; v5
typos fixed, matches published versio
A dynamical system approach to higher order gravity
The dynamical system approach has recently acquired great importance in the
investigation on higher order theories of gravity. In this talk I review the
main results and I give brief comments on the perspectives for further
developments.Comment: 6 pages, 1 figure, 2 tables, talk given at IRGAC 2006, July 200
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