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 $f(R)$ gravity. It is found that only one class of $f(R)$ 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 $c_s^2>\frac{\sqrt{5}-1}{6}\approx 0.21$. This result is remarkably similar to the GR case, where it was found that the Einstein Static model is stable for $c_s^2>{1/5}$.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 ($E_{ab}$) and magnetic ($H_{ab}$) 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, $E_{ab}$ is related to the harmonic components of the gravitational potential $\Phi_k$ and the usual dominant Sachs-Wolfe contribution $\delta T_R/\bar{T}_R\sim\Phi_k$ 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