Role of initial data in spherical collapse

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, which includes most of the known physical forms of matter. It is shown that given the distribution of the density and pressure profiles at the initial surface from which the collapse evolves, there is a freedom in choosing rest of the free functions, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. It is thus seen that it is the initial data that determines the end state of spherical collapse in terms of these outcomes, and we get a good picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review

An inhomogeneous alternative to dark energy?

Recently, there have been suggestions that the apparent accelerated expansion of the universe is not caused by repulsive gravitation due to dark energy, but is rather a result of inhomogeneities in the distribution of matter. In this work, we investigate the behaviour of a dust dominated inhomogeneous Lemaitre-Tolman-Bondi universe model, and confront it with various astrophysical observations. We find that such a model can easily explain the observed luminosity distance-redshift relation of supernovae without the need for dark energy, when the inhomogeneity is in the form of an underdense bubble centered near the observer. With the additional assumption that the universe outside the bubble is approximately described by a homogeneous Einstein-de Sitter model, we find that the position of the first CMB peak can be made to match the WMAP observations. Whether or not it is possible to reproduce the entire CMB angular power spectrum in an inhomogeneous model without dark energy, is still an open question.Comment: 8 pages (REVTeX4), 4 figures. v2: Minor changes to text plus added some references. Accepted for publication in PR

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

The radial BAO scale and Cosmic Shear, a new observable for Inhomogeneous Cosmologies

As an alternative explanation of the dimming of distant supernovae it has recently been advocated that we live in a special place in the Universe near the centre of a large spherical void described by a Lemaitre-Tolman-Bondi (LTB) metric. In this scenario, the Universe is no longer homogeneous and isotropic, and the apparent late time acceleration is actually a consequence of spatial gradients. We propose in this paper a new observable, the normalized cosmic shear, written in terms of directly observable quantities, and calculable in arbitrary inhomogeneous cosmologies. This will allow future surveys to determine whether we live in a homogeneous universe or not. In this paper we also update our previous observational constraints from geometrical measures of the background cosmology. We include the Union Supernovae data set of 307 Type Ia supernovae, the CMB acoustic scale and the first measurement of the radial baryon acoustic oscillation scale. Even though the new data sets are significantly more constraining, LTB models -- albeit with slightly larger voids -- are still in excellent agreement with observations, at chi^2/d.o.f. = 307.7/(310-4)=1.005. Together with the paper we also publish the updated easyLTB code used for calculating the models and for comparing them to the observations.Comment: 18 pages, 8 figures, the code can be downloaded at http://www.phys.au.dk/~haugboel/software.shtm

"Swiss-Cheese" Inhomogeneous Cosmology & the Dark Energy Problem

We study an exact swiss-cheese model of the Universe, where inhomogeneous LTB patches are embedded in a flat FLRW background, in order to see how observations of distant sources are affected. We find negligible integrated effect, suppressed by (L/R_{H})^3 (where L is the size of one patch, and R_{H} is the Hubble radius), both perturbatively and non-perturbatively. We disentangle this effect from the Doppler term (which is much larger and has been used recently \cite{BMN} to try to fit the SN curve without dark energy) by making contact with cosmological perturbation theory.Comment: 35 pages, 6 figure

LTB solutions in Newtonian gauge: from strong to weak fields

Lemaitre-Tolman-Bondi (LTB) solutions are used frequently to describe the collapse or expansion of spherically symmetric inhomogeneous mass distributions in the Universe. These exact solutions are obtained in the synchronous gauge where nonlinear dynamics (with respect to the FLRW background) induce large deviations from the FLRW metric. In this paper we show explicitly that this is a gauge artefact (for realistic sub-horizon inhomogeneities). We write down the nonlinear gauge transformation from synchronous to Newtonian gauge for a general LTB solution using the fact that the peculiar velocities are small. In the latter gauge we recover the solution in the form of a weakly perturbed FLRW metric that is assumed in standard cosmology. Furthermore we show how to obtain the LTB solutions directly in Newtonian gauge and illustrate how the Newtonian approximation remains valid in the nonlinear regime where cosmological perturbation theory breaks down. Finally we discuss the implications of our results for the backreaction scenario.Comment: 17 page

Stability and quasi-normal modes of charged black holes in Born-Infeld gravity

In this paper we study the stability and quasi-normal modes of scalar perturbations of black holes. The static charged black hole considered here is a solution to Born-Infeld electrodynamics coupled to gravity. We conclude that the black hole is stable. We also compare the stability of it with its linear counter-part Reissner-Nordstrom black hole. The quasi-normal modes are computed using the WKB method. The behavior of these modes with the non-linear parameter, temperature, mass of the scalar field and the spherical index are analyzed in detail.Comment: Latex, 17 pages, 13 figures, some sections edited, references adde

Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0

In this paper, instead of invoking Dark Energy, we try and fit various cosmological observations with a large Gpc scale under-dense region (Void) which is modeled by a Lemaitre-Tolman-Bondi metric that at large distances becomes a homogeneous FLRW metric. We improve on previous analyses by allowing for nonzero overall curvature, accurately computing the distance to the last-scattering surface and the observed scale of the Baryon Acoustic peaks, and investigating important effects that could arise from having nontrivial Void density profiles. We mainly focus on the WMAP 7-yr data (TT and TE), Supernova data (SDSS SN), Hubble constant measurements (HST) and Baryon Acoustic Oscillation data (SDSS and LRG). We find that the inclusion of a nonzero overall curvature drastically improves the goodness of fit of the Void model, bringing it very close to that of a homogeneous universe containing Dark Energy, while by varying the profile one can increase the value of the local Hubble parameter which has been a challenge for these models. We also try to gauge how well our model can fit the large-scale-structure data, but a comprehensive analysis will require the knowledge of perturbations on LTB metrics. The model is consistent with the CMB dipole if the observer is about 15 Mpc off the centre of the Void. Remarkably, such an off-center position may be able to account for the recent anomalous measurements of a large bulk flow from kSZ data. Finally we provide several analytical approximations in different regimes for the LTB metric, and a numerical module for CosmoMC, thus allowing for a MCMC exploration of the full parameter space.Comment: 70 pages, 12 figures, matches version accepted for publication in JCAP. References added, numerical values in tables changed due to minor bug, conclusions unaltered. Numerical module available at http://web.physik.rwth-aachen.de/download/valkenburg