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.

Testing homogeneity with galaxy number counts : light-cone metric and general low-redshift expansion for a central observer in a matter dominated isotropic universe without cosmological constant

As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test this hypothesis we calculate the general analytical formula to fifth order for the redshift spherical shell mass. Using the same analytical method we write the metric in the light-cone by introducing a gauge invariant quantity $G(z)$ which together with the luminosity distance $D_L(z)$ completely determine the light-cone geometry of a LTB model.Comment: 13 page

Late time solutions for inhomogeneous Lambda-CDM cosmology, their characterization and observation

Assuming homogeneous isotropic Lambda-CDM cosmology allows Lambda, spatial curvature and dark matter density to be inferred from large scale structure observations such as supernovae. The purpose of this paper is to extend this to allow observations to measure or constrain inhomogeneity and anisotropy. We obtain the general inhomogeneous anisotropic Lambda-CDM solution which is locally asymptotic to an expanding de Sitter solution as a late time expansion using Starobinsky's method (analogous to the `holographic renormalization' technique in AdS/CFT) together with a resummation of the series. The dark matter is modeled as perfect dust fluid. The terms in the expansion systematically describe inhomogeneous and anisotropic deformations of an expanding FLRW solution, and are given as a spatial derivative expansion in terms of data characterizing the solution - a 3-metric and a perturbation of that 3-metric. Leading terms describe inhomogeneity and anisotropy on the scale set by the cosmological constant, approximately the horizon scale today. Higher terms in the expansion describe shorter scale variations. We compute the luminosity distance-redshift relation and argue that comparison with current and future observation would allow a partial reconstruction of the characterizing data. We also comment on smoothing these solutions noting that geometric flows (such as Ricci flow) applied to the characterizing data provide a canonical averaging method.Comment: 15 pages, 2 figures; v2: minor corrections and improvements, references adde

Can the Copernican principle be tested by cosmic neutrino background?

The Copernican principle, stating that we do not occupy any special place in our universe, is usually taken for granted in modern cosmology. However recent observational data of supernova indicate that we may live in the under-dense center of our universe, which makes the Copernican principle challenged. It thus becomes urgent and important to test the Copernican principle via cosmological observations. Taking into account that unlike the cosmic photons, the cosmic neutrinos of different energies come from the different places to us along the different worldlines, we here propose cosmic neutrino background as a test of the Copernican principle. It is shown that from the theoretical perspective cosmic neutrino background can allow one to determine whether the Copernican principle is valid or not, but to implement such an observation the larger neutrino detectors are called for.Comment: JHEP style, 10 pages, 4 figures, version to appear in JCA

Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable?

As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test such an hypothesis we calculate the low redshift expansion of the luminosity distance $D_L(z)$ and the redshift spherical shell mass density $mn(z)$ for a central observer in a LTB space without cosmological constant and show how they cannot fit the observations implied by a $\Lambda CDM$ model if the conditions to avoid a weak central singularity are imposed, i.e. if the matter distribution is smooth everywhere. Our conclusions are valid for any value of the cosmological constant, not only for $\Omega_{\Lambda}>1/3$ as implied by previous proofs that $q^{app}_0$ has to be positive in a smooth LTB space, based on considering only the luminosity distance. The observational signatures of smooth LTB matter dominated models are fundamentally different from the ones of $\Lambda CDM$ models not only because it is not possible to reproduce a negative apparent central deceleration $q^{app}_0$, but because of deeper differences in their space-time geometry which make impossible the inversion problem when more than one observable is considered, and emerge at any redshift, not only for $z=0$.Comment: 18 pages, corrected a typo in the definition of the energy density which doesn't change the conclusion, references adde

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

Lemaitre-Tolman-Bondi dust spacetimes: Symmetry properties and some extensions to the dissipative case

We consider extensions of Lemaitre-Tolman-Bondi (LTB) spacetimes to the dissipative case. For doing that we previously carry out a systematic study on LTB. This study is based on two different aspects of LTB. On the one hand, a symmetry property of LTB will be presented. On the other hand, the description of LTB in terms of some fundamental scalar functions (structure scalars) appearing in the orthogonal splitting of Riemann tensor will be provided. We shall consider as "natural" generalizations of LTB (hereafter referred to as GLTB) either those metrics admitting some similar kind of symmetry as LTB, or those sharing structure scalars with similar dependence on the metric.Comment: 13 pages RevTex. To appear in Phys. Rev. D. Some references corrected and update

ZOBOV: a parameter-free void-finding algorithm

ZOBOV (ZOnes Bordering On Voidness) is an algorithm that finds density depressions in a set of points, without any free parameters, or assumptions about shape. It uses the Voronoi tessellation to estimate densities, which it uses to find both voids and subvoids. It also measures probabilities that each void or subvoid arises from Poisson fluctuations. This paper describes the ZOBOV algorithm, and the results from its application to the dark-matter particles in a region of the Millennium Simulation. Additionally, the paper points out an interesting high-density peak in the probability distribution of dark-matter particle densities.Comment: 10 pages, 8 figures, MNRAS, accepted. Added explanatory figures, and better edge-detection methods. ZOBOV code available at http://www.ifa.hawaii.edu/~neyrinck/vobo

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

Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?

We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data almost as well as the LCDM model without requiring a dark energy component. The Szekeres models were originally derived as an exact solution to Einstein's equations with a general metric that has no symmetries and are regarded as good candidates to model the true lumpy universe that we observe. The null geodesics in these models are not radial. The best fit model found is also consistent with the requirement of spatial flatness at CMB scales. The first results presented here seem to encourage further investigations of apparent acceleration using various inhomogeneous models and other constraints from CMB and large structure need to be explored next.Comment: 6 pages, 1 figure, matches version published in PR