Forecasting inflation in France.

The paper develops a model for forecasting inflation in France. As this model has to be integrated in the Eurosystem projection exercises, the projections are conditional to specific assumptions and must be consistent with the Macroeconomic projection exercise of the Banque de France. The specification of the model is thus highly constrained. The theoretical foundations of the model are based on the markup model for prices, but the resulting empirical model also has elements relating to the purchasing power parity and the Phillips curve. The model aggregates forecasts of the main HICP subcomponents. We show that the model exhibits better performance than a standard AR(4) model.Inflation , Out-of-sample forecast , Economic modelling.

Compensation in the Financial Sector: Are all Bankers Superstars?

Based on a survey among French engineers, I find that employees in the financial sector are highly paid. I also find large pay differences within the sector and that a large share of compensation is variable. I consider three potential models accounting for these facts: a model of superstars (Rosen, 1981), a model of compensating wage differential (Lucas, 1977), and a model of moral hazard (Laffont and Martimort, 2002). I investigate and test the empirical implications of these models. I conclude that the model of superstars fits better the data than the models of moral hazard and compensating wage differential.Finance, compensation ; wage distribution ; wage structure ; incentives, superstars

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.

The Pauli equation in scale relativity

In standard quantum mechanics, it is not possible to directly extend the Schrodinger equation to spinors, so the Pauli equation must be derived from the Dirac equation by taking its non-relativistic limit. Hence, it predicts the existence of an intrinsic magnetic moment for the electron and gives its correct value. In the scale relativity framework, the Schrodinger, Klein-Gordon and Dirac equations have been derived from first principles as geodesics equations of a non-differentiable and continuous spacetime. Since such a generalized geometry implies the occurence of new discrete symmetry breakings, this has led us to write Dirac bi-spinors in the form of bi-quaternions (complex quaternions). In the present work, we show that, in scale relativity also, the correct Pauli equation can only be obtained from a non-relativistic limit of the relativistic geodesics equation (which, after integration, becomes the Dirac equation) and not from the non-relativistic formalism (that involves symmetry breakings in a fractal 3-space). The same degeneracy procedure, when it is applied to the bi-quaternionic 4-velocity used to derive the Dirac equation, naturally yields a Pauli-type quaternionic 3-velocity. It therefore corroborates the relevance of the scale relativity approach for the building from first principles of the quantum postulates and of the quantum tools. This also reinforces the relativistic and fundamentally quantum nature of spin, which we attribute in scale relativity to the non-differentiability of the quantum spacetime geometry (and not only of the quantum space). We conclude by performing numerical simulations of spinor geodesics, that allow one to gain a physical geometric picture of the nature of spin.Comment: 22 pages, 2 figures, accepted for publication in J. Phys. A: Math. & Ge

Average observational quantities in the timescape cosmology

We examine the properties of a recently proposed observationally viable alternative to homogeneous cosmology with smooth dark energy, the timescape cosmology. In the timescape model cosmic acceleration is realized as an apparent effect related to the calibration of clocks and rods of observers in bound systems relative to volume-average observers in an inhomogeneous geometry in ordinary general relativity. The model is based on an exact solution to a Buchert average of the Einstein equations with backreaction. The present paper examines a number of observational tests which will enable the timescape model to be distinguished from homogeneous cosmologies with a cosmological constant or other smooth dark energy, in current and future generations of dark energy experiments. Predictions are presented for: comoving distance measures; H(z); the equivalent of the dark energy equation of state, w(z); the Om(z) measure of Sahni, Shafieloo and Starobinsky; the Alcock-Paczynski test; the baryon acoustic oscillation measure, D_v; the inhomogeneity test of Clarkson, Bassett and Lu; and the time drift of cosmological redshifts. Where possible, the predictions are compared to recent independent studies of similar measures in homogeneous cosmologies with dark energy. Three separate tests with indications of results in possible tension with the Lambda CDM model are found to be consistent with the expectations of the timescape cosmology.Comment: 22 pages, 12 figures; v2 discussion, references added, matches published versio

Tidal Dynamics in Cosmological Spacetimes

We study the relative motion of nearby free test particles in cosmological spacetimes, such as the FLRW and LTB models. In particular, the influence of spatial inhomogeneities on local tidal accelerations is investigated. The implications of our results for the dynamics of the solar system are briefly discussed. That is, on the basis of the models studied in this paper, we estimate the tidal influence of the cosmic gravitational field on the orbit of the Earth around the Sun and show that the corresponding temporal rate of variation of the astronomical unit is negligibly small.Comment: 12 pages, no figures, REVTeX 4.0; appendix added, new references, and minor changes throughout; to appear in Classical and Quantum Gravity; v4: error in (A24) of Appendix A corrected, results and conclusions unchanged. We thank L. Iorio for pointing out the erro

Generalized quantum potentials in scale relativity

We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard quantum constant hbar) is equivalent to a generalized Schrodinger equation. Then we show that, even in the case of the presence of vorticity, it is also possible to obtain, for a large class of systems, a Schrodinger-like equation of the vectorial field type from the continuity and Euler equations including a quantum potential. The same kind of transformation also applies to a classical charged fluid subjected to an electromagnetic field and to an additional potential having the form of a quantum potential. Such a fluid can therefore be described by an equation of the Ginzburg-Landau type, and is expected to show some superconducting-like properties. Moreover, a Schrodinger form can be obtained for the fluctuating rotational motion of a solid. In this case the mass is replaced by the tensor of inertia, and a generalized form of the quantum potential is derived. We finally reconsider the case of a standard diffusion process, and we show that, after a change of variable, the diffusion equation can also be given the form of a continuity and Euler system including an additional potential energy. Since this potential is exactly the opposite of a quantum potential, the quantum behavior may be considered, in this context, as an anti-diffusion.Comment: 33 pages, submitted for publicatio

The Cosmic Microwave Background in an Inhomogeneous Universe - why void models of dark energy are only weakly constrained by the CMB

The dimming of Type Ia supernovae could be the result of Hubble-scale inhomogeneity in the matter and spatial curvature, rather than signaling the presence of a dark energy component. A key challenge for such models is to fit the detailed spectrum of the cosmic microwave background (CMB). We present a detailed discussion of the small-scale CMB in an inhomogeneous universe, focusing on spherically symmetric `void' models. We allow for the dynamical effects of radiation while analyzing the problem, in contrast to other work which inadvertently fine tunes its spatial profile. This is a surprisingly important effect and we reach substantially different conclusions. Models which are open at CMB distances fit the CMB power spectrum without fine tuning; these models also fit the supernovae and local Hubble rate data which favours a high expansion rate. Asymptotically flat models may fit the CMB, but require some extra assumptions. We argue that a full treatment of the radiation in these models is necessary if we are to understand the correct constraints from the CMB, as well as other observations which rely on it, such as spectral distortions of the black body spectrum, the kinematic Sunyaev-Zeldovich effect or the Baryon Acoustic Oscillations.Comment: 23 pages with 14 figures. v2 has considerably extended discussion and analysis, but the basic results are unchanged. v3 is the final versio

Model- and calibration-independent test of cosmic acceleration

We present a calibration-independent test of the accelerated expansion of the universe using supernova type Ia data. The test is also model-independent in the sense that no assumptions about the content of the universe or about the parameterization of the deceleration parameter are made and that it does not assume any dynamical equations of motion. Yet, the test assumes the universe and the distribution of supernovae to be statistically homogeneous and isotropic. A significant reduction of systematic effects, as compared to our previous, calibration-dependent test, is achieved. Accelerated expansion is detected at significant level (4.3 sigma in the 2007 Gold sample, 7.2 sigma in the 2008 Union sample) if the universe is spatially flat. This result depends, however, crucially on supernovae with a redshift smaller than 0.1, for which the assumption of statistical isotropy and homogeneity is less well established.Comment: 13 pages, 2 figures, major change

Systematic corrections to the measured cosmological constant as a result of local inhomogeneity

We calculate the systematic inhomogeneity-induced correction to the cosmological constant that one would infer from an analysis of the luminosities and redshifts of Type Ia supernovae, assuming a homogeneous universe. The calculation entails a post-Newtonian expansion within the framework of second order perturbation theory, wherein we consider the effects of subhorizon density perturbations in a flat, dust dominated universe. Within this formalism, we calculate luminosity distances and redshifts along the past light cone of an observer. The resulting luminosity distance-redshift relation is fit to that of a homogeneous model in order to deduce the best-fit cosmological constant density Omega_Lambda. We find that the luminosity distance-redshift relation is indeed modified, by a small fraction of order 10^{-5}. When fitting this perturbed relation to that of a homogeneous universe, we find that the inferred cosmological constant can be surprisingly large, depending on the range of redshifts sampled. For a sample of supernovae extending from z=0.02 out to z=0.15, we find that Omega_Lambda=0.004. The value of Omega_Lambda has a large variance, and its magnitude tends to get larger for smaller redshifts, implying that precision measurements from nearby supernova data will require taking this effect into account. However, we find that this effect is likely too small to explain the observed value of Omega_Lambda=0.7. There have been previous claims of much larger backreaction effects. By contrast to those calculations, our work is directly related to how observers deduce cosmological parameters from astronomical data.Comment: 28 pages, 3 figures, revtex4; v2: corrected comments and the section on previous work; v3: clarified wording. References adde