Timelike and null focusing singularities in spherical symmetry: a solution to the cosmological horizon problem and a challenge to the cosmic censorship hypothesis

Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated in SI93, we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: $p={1\over 3} \rho$) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and to the Strong Cosmic Censorship Hypothesis to which we propose a class of physically consistent counter-examples.Comment: 26 pages, 2 figures, LaTeX file. Submitted to Phys. Rev.

Testing the Copernican and Cosmological Principles in the local universe with galaxy surveys

Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle. A spatially inhomogeneous matter distribution can be compatible with the Copernican Principle but not with the stronger version of it, the Cosmological Principle which requires the additional hypothesis of spatial homogeneity. We establish criteria for testing that a given density field, in a finite sample at low redshifts, is statistically and/or spatially homogeneous. The basic question to be considered is whether a distribution is, at different spatial scales, self-averaging. This can be achieved by studying the probability density function of conditional fluctuations. We find that galaxy structures in the SDSS samples, the largest currently available, are spatially inhomogeneous but statistically homogeneous and isotropic up to ~ 100 Mpc/h. Evidences for the breaking of self-averaging are found up to the largest scales probed by the SDSS data. The comparison between the results obtained in volumes of different size allows us to unambiguously conclude that the lack of elf-averaging is induced by finite-size effects due to long-range correlated fluctuations. We finally discuss the relevance of these results from the point of view of cosmological modeling.Comment: 12 pages, 3 figures, accepted for publication in JCA

How close can an Inhomogeneous Universe mimic the Concordance Model?

Recently, spatially inhomogeneous cosmological models have been proposed as an alternative to the LCDM model, with the aim of reproducing the late time dynamics of the Universe without introducing a cosmological constant or dark energy. This paper investigates the possibility of distinguishing such models from the standard LCDM using background or large scale structure data. It also illustrates and emphasizes the necessity of testing the Copernican principle in order to confront the tests of general relativity with the large scale structure.Comment: 15 pages, 7 figure

The Scale of Cosmic Isotropy

The most fundamental premise to the standard model of the universe, the Cosmological Principle (CP), states that the large-scale properties of the universe are the same in all directions and at all comoving positions. Demonstrating this theoretical hypothesis has proven to be a formidable challenge. The cross-over scale R_{iso} above which the galaxy distribution becomes statistically isotropic is vaguely defined and poorly (if not at all) quantified. Here we report on a formalism that allows us to provide an unambiguous operational definition and an estimate of R_{iso}. We apply the method to galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 7, finding that R_{iso}\sim 150h^{-1} Mpc. Besides providing a consistency test of the Copernican principle, this result is in agreement with predictions based on numerical simulations of the spatial distribution of galaxies in cold dark matter dominated cosmological models.Comment: 15 pages, 4 figures, accepted by JCAP. The text matches the published versio

An Inhomogeneous Model Universe Behaving Homogeneously

We present a new model universe based on the junction of FRW to flat Lemaitre-Tolman-Bondi (LTB) solutions of Einstein equations along our past light cone, bringing structures within the FRW models. The model is assumed globally to be homogeneous, i.e. the cosmological principle is valid. Local inhomogeneities within the past light cone are modeled as a flat LTB, whereas those outside the light cone are assumed to be smoothed out and represented by a FRW model. The model is singularity free, always FRW far from the observer along the past light cone, gives way to a different luminosity distance relation as for the CDM/FRW models, a negative deceleration parameter near the observer, and correct linear and non-linear density contrast. As a whole, the model behaves like a FRW model on the past light cone with a special behavior of the scale factor, Hubble and deceleration parameter, mimicking dark energy.Comment: 23 pages, 19 figures, published version in GR

Testing the Copernican Principle via Cosmological Observations

Observations of distances to Type-Ia supernovae can be explained by cosmological models that include either a gigaparsec-scale void, or a cosmic flow, without the need for Dark Energy. Instead of invoking dark energy, these inhomogeneous models instead violate the Copernican Principle. we show that current cosmological observations (Supernovae, Baryon Acoustic Oscillations and estimates of the Hubble parameters based on the age of the oldest stars) are not able to rule out inhomogeneous anti-Copernican models. The next generation of surveys for baryonic acoustic oscillations will be sufficiently precise to either validate the Copernican Principle or determine the existence of a local Gpc scale inhomogeneity.Comment: 16 pages, 9 figures; accepted for publication in JCA

Imitating accelerated expansion of the Universe by matter inhomogeneities - corrections of some misunderstandings

A number of misunderstandings about modeling the apparent accelerated expansion of the Universe, and about the `weak singularity' are clarified: 1. Of the five definitions of the deceleration parameter given by Hirata and Seljak (HS), only $q_1$ is a correct invariant measure of acceleration/deceleration of expansion. The $q_3$ and $q_4$ are unrelated to acceleration in an inhomogeneous model. 2. The averaging over directions involved in the definition of $q_4$ does not correspond to what is done in observational astronomy. 3. HS's equation (38) connecting $q_4$ to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lema\^{\i}tre-Tolman (L-T) model. The intermediate equation (31) that determines $q_{3'}$ is correct, but approximate, so it cannot be used for determining the sign of the deceleration parameter. Even so, at the centre of symmetry of the L-T model, it puts no limitation on the sign of $q_{3'}(0)$. 4. The `weak singularity' of Vanderveld {\it et al.} is a conical profile of mass density at the centre - a perfectly acceptable configuration. 5. The so-called `critical point' in the equations of the `inverse problem' for a central observer in an L-T model is a manifestation of the apparent horizon - a common property of the past light cones in zero-lambda L-T models, perfectly manageable if the equations are correctly integrated.Comment: 15 pages. Completely rewritten to match the published version. We added discussion of 2 key papers cited by VFW and identified more clearly the assumptions, approximations and mistakes that led to certain misconceptions

New exact stationary cylindrical anisotropic fluid solution of GR

International audienceIn a previous paper, the properties of interior spacetimes sourced by stationary cylindrical anisotropic fluids have been analytically studied for both nonrigid and rigid rotation. The gravito-electromagnetic features of different classes of such GR solutions have been described. Their regularity conditions and those for their junction to a vacuum exterior have also been provided. A new class of rigidly rotating exact solutions to Einstein’s field equations satisfying a physically consistent equation of state for anisotropic fluids is displayed here. Its physical properties are discussed