Vente à distance, internet et dynamique des prix.

The share of retail sales made via distance selling has increased steadily, driven by Internet sales. Meanwhile, a large body of research has been devoted to measuring the impact of online shopping on consumer prices. These studies are based primarily on microeconomic data and they reveal contrasting effects due to diverging microeconomic behaviours. This paper aims to use a macro-sector estimation to show how the price-decreasing effects of Internet shopping outweigh the price-increasing effects. In that purpose, we use French price index series and distance selling sales covering about 30 sectors, from 1990 to 2007. We find that downward effects dominate: the recent development of distance selling, due to the development of online selling, results in lower prices.E-Commerce, Price, Competition.

Can we avoid dark energy?

The idea that we live near the centre of a large, nonlinear void has attracted attention recently as an alternative to dark energy or modified gravity. We show that an appropriate void profile can fit both the latest cosmic microwave background and supernova data. However, this requires either a fine-tuned primordial spectrum or a Hubble rate so low as to rule these models out. We also show that measurements of the radial baryon acoustic scale can provide very strong constraints. Our results present a serious challenge to void models of acceleration.Comment: 5 pages, 4 figures; minor changes; version published in Phys. Rev. Let

Can decaying modes save void models for acceleration?

The unexpected dimness of Type Ia supernovae (SNe), apparently due to accelerated expansion driven by some form of dark energy or modified gravity, has led to attempts to explain the observations using only general relativity with baryonic and cold dark matter, but by dropping the standard assumption of homogeneity on Hubble scales. In particular, the SN data can be explained if we live near the centre of a Hubble-scale void. However, such void models have been shown to be inconsistent with various observations, assuming the void consists of a pure growing mode. Here it is shown that models with significant decaying mode contribution today can be ruled out on the basis of the expected cosmic microwave background spectral distortion. This essentially closes one of the very few remaining loopholes in attempts to rule out void models, and strengthens the evidence for Hubble-scale homogeneity.Comment: 11 pages, 3 figures; discussion expanded, appendix added; version accepted to Phys. Rev.

Precision cosmology defeats void models for acceleration

The suggestion that we occupy a privileged position near the centre of a large, nonlinear, and nearly spherical void has recently attracted much attention as an alternative to dark energy. Putting aside the philosophical problems with this scenario, we perform the most complete and up-to-date comparison with cosmological data. We use supernovae and the full cosmic microwave background spectrum as the basis of our analysis. We also include constraints from radial baryonic acoustic oscillations, the local Hubble rate, age, big bang nucleosynthesis, the Compton y-distortion, and for the first time include the local amplitude of matter fluctuations, \sigma_8. These all paint a consistent picture in which voids are in severe tension with the data. In particular, void models predict a very low local Hubble rate, suffer from an "old age problem", and predict much less local structure than is observed.Comment: 22 pages, 12 figures; v2 adds models in closed backgrounds; conclusions strengthened; version accepted to Phys. Rev.

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

Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae

It is now a known fact that if we happen to be living in the middle of a large underdense region, then we will observe an "apparent acceleration", even when any form of dark energy is absent. In this paper, we present a "Minimal Void" scenario, i.e. a "void" with minimal underdensity contrast (of about -0.4) and radius (~ 200-250 Mpc/h) that can, not only explain the supernovae data, but also be consistent with the 3-yr WMAP data. We also discuss consistency of our model with various other measurements such as Big Bang Nucleosynthesis, Baryon Acoustic Oscillations and local measurements of the Hubble parameter, and also point out possible observable signatures.Comment: Minor numerical errors and typos corrected, references adde

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 growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era

This study belongs to a series devoted to using Szekeres inhomogeneous models to develop a theoretical framework where observations can be investigated with a wider range of possible interpretations. We look here into the growth of large-scale structure in the models. The Szekeres models are exact solutions to Einstein's equations that were originally derived with no symmetries. We use a formulation of the models that is due to Goode and Wainwright, who considered the models as exact perturbations of an FLRW background. Using the Raychaudhuri equation, we write for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact non-linear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres non-linear perturbations. The growth is also stronger than that of the non-linear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today (abridged)Comment: 18 pages, 4 figures, matches PRD accepted versio

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

A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized by a constant equation of state parameter $w$ and a very accurate approximation for the Ansatz $w(a)=w_0+w_a(1-a)$. We compute the growth index \gamma=\log f(a)/\log\Om_m(a), and its redshift dependence, using the exact and approximate solutions in terms of Legendre polynomials and show that it can be parametrized as $\gamma(a)=\gamma_0+\gamma_a(1-a)$ in most cases. We then compare four different types of dark energy (DE) models: $w\Lambda$CDM, DGP, $f(R)$ and a LTB-large-void model, which have very different behaviors at z\gsim1. This allows us to study the possibility to differentiate between different DE alternatives using wide and deep surveys like Euclid, which will measure both photometric and spectroscopic redshifts for several hundreds of millions of galaxies up to redshift $z\simeq 2$. We do a Fisher matrix analysis for the prospects of differentiating among the different DE models in terms of the growth index, taken as a given function of redshift or with a principal component analysis, with a value for each redshift bin for a Euclid-like survey. We use as observables the complete and marginalized power spectrum of galaxies $P(k)$ and the Weak Lensing (WL) power spectrum. We find that, using $P(k)$, one can reach (2%, 5%) errors in $(w_0, w_a)$, and (4%, 12%) errors in $(\gamma_0, \gamma_a)$, while using WL we get errors at least twice as large. These estimates allow us to differentiate easily between DGP, $f(R)$ models and $\Lambda$CDM, while it would be more difficult to distinguish the latter from a variable equation of state parameter or LTB models using only the growth index.}Comment: 29 pages, 7 figures, 6 table