A Qualitative and Quantitative Evaluation of 8 Clear Sky Models

We provide a qualitative and quantitative evaluation of 8 clear sky models used in Computer Graphics. We compare the models with each other as well as with measurements and with a reference model from the physics community. After a short summary of the physics of the problem, we present the measurements and the reference model, and how we "invert" it to get the model parameters. We then give an overview of each CG model, and detail its scope, its algorithmic complexity, and its results using the same parameters as in the reference model. We also compare the models with a perceptual study. Our quantitative results confirm that the less simplifications and approximations are used to solve the physical equations, the more accurate are the results. We conclude with a discussion of the advantages and drawbacks of each model, and how to further improve their accuracy

On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity

Field theories whose full action is Lorentz invariant (or diffeomorphism invariant) can exhibit superluminal behaviors through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagations is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories, and we stress the role played by the Cauchy problem and the notions of chronology and time arrow. We show that superluminal behavior threaten causality only if a prior chronology on spacetime is chosen. In the case where superluminal propagations occur, however, there is at least two non conformally related metrics on spacetime and thus two available notions of chronology. These two chronologies are on equal footing and it would thus be misleading to choose \textit{ab initio} one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. We actually show that superluminal propagations do not threaten causality. As an illustration of these conceptual issues, we consider two field theories, namely k-essences scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, MOND-like theories of gravity and varying speed of light theories.Comment: 15 pages, 2 figures; minor changes, references added, submitted to Phys.Rev.

The two-body problem: analytical results in a toy-model of relativistic gravity

The two body problem in a scalar theory of gravity is investigated. We focus on the closest theory to General Relativity (GR), namely Nordstr\"om's theory of gravity (1913). The gravitational field can be exactly solved for any configuration of point-particles. We then derive the exact equations of motion of two inspiraling bodies including the exact self-forces terms. We prove that there is no innermost circular orbit (ICO) in the exact theory whereas we find (order-dependent) ICOs if post-Newtonian (PN) truncations are used. We construct a solution of the two body problem in an iterative (non-PN) way, which can be viewed as a series in powers of $(v/c)^{5}$. Besides this rapid convergence, each order also provides non-perturbative information. Starting from a circular Newtonian-like orbit, the first iteration already yields the 4.5 PN radiation reaction. These results not only shed light on some non-perturbative effects of relativistic gravity, but may also be useful to test numerical codes.Comment: 7 Figures, To appear in the proceedings of Albert Einstein's Century International Conference, Paris, France, 18-22 Jul

Causality and Superluminal Fields

The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related metrics over spacetime. Although tempting, a definitive choice of a preferred metric to which one may refer to is not satisfying. It would indeed be in great conflict with the spirit of general covariance. Moreover, a theory which appear to be non causal with respect to (hereafter, w.r.t) this metric, may well be causal w.r.t another metric. In a theory involving fields that propagate at different speeds (e.g. due to some spontaneous breaking of Lorentz invariance), spacetime is endowed with such a finite set of non-conformally related metrics. In that case one must look for a new notion of causality, such that 1. no particular metric is favored and 2. there is an unique answer to the question : ``is the theory causal?''. This new causality is unique and defined w.r.t the metric drawing the wider cone in the tangent space of a given point of the manifold. Moreover, which metric defines the wider cone may depend on the location on spacetime. In that sense, superluminal fields are generically causal, provided that some other basic requirements are met.Comment: 3 pages, Prepared for the Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, Berlin, Germany, 23-27 July 2006; document class change

Field-theoretical formulations of MOND-like gravity

Modified Newtonian dynamics (MOND) is a possible way to explain the flat galaxy rotation curves without invoking the existence of dark matter. It is however quite difficult to predict such a phenomenology in a consistent field theory, free of instabilities and admitting a well-posed Cauchy problem. We examine critically various proposals of the literature, and underline their successes and failures both from the experimental and the field-theoretical viewpoints. We exhibit new difficulties in both cases, and point out the hidden fine tuning of some models. On the other hand, we show that several published no-go theorems are based on hypotheses which may be unnecessary, so that the space of possible models is a priori larger. We examine a new route to reproduce the MOND physics, in which the field equations are particularly simple outside matter. However, the analysis of the field equations within matter (a crucial point which is often forgotten in the literature) exhibits a deadly problem, namely that they do not remain always hyperbolic. Incidentally, we prove that the same theoretical framework provides a stable and well-posed model able to reproduce the Pioneer anomaly without spoiling any of the precision tests of general relativity. Our conclusion is that all MOND-like models proposed in the literature, including the new ones examined in this paper, present serious difficulties: Not only they are unnaturally fine tuned, but they also fail to reproduce some experimental facts or are unstable or inconsistent as field theories. However, some frameworks, notably the tensor-vector-scalar (TeVeS) one of Bekenstein and Sanders, seem more promising than others, and our discussion underlines in which directions one should try to improve them.Comment: 66 pages, 6 figures, RevTeX4 format, version reflecting the changes in the published pape

Béarnais émigrés en Amérique : des marges qui résistent?

Les Français qui émigrèrent vers les Amériques au xixe siècle furent très largement issus des marges géographiques de la France, le plus fort contingent étant fourni par les groupes basques, béarnais et bigourdans originaires des Pyrénées occidentales. Si des observateurs ont remarqué que des groupes de migrants conservaient, voire revivifiaient leurs traditions culturelles dans les pays d’arrivée, il ne semble pas en avoir été de même pour les Béarnais et les Bigourdans. (Nous laisserons de côté les Basques qui, par leur langue et statut spécifiques, ainsi que par le rôle de l’Église catholique, furent davantage amenés à maintenir, en l’organisant, leur identité.) Si l’on se base principalement sur les lettres de ces émigrés, il apparaît que l’identité béarnaise à la première génération se maintient dans un entre-soi à travers la perpétuation du parler béarnais, de la cuisine locale, de la pratique de certains jeux, et s’exprime et se renforce au travers d’un fort lobbying; en revanche, dès qu’il s’agit de présentation de soi dans la société environnante (par les vêtements notamment), on observe le souci de ne pas se singulariser; par ailleurs, quand les émigrés créent des sociétés d’entraide, c’est sous la bannière française qu’ils le font. On se demandera alors si la perpétuation de leurs traits culturels, plus que l’affirmation d’une identité, ne correspondait pas surtout à la nécessité de renforcement d’un groupe, tremplin et gage de l’intégration souhaitée. Cette hypothèse sera replacée dans la nature et l’époque de l’émigration pyrénéenne

Trispectrum versus Bispectrum in Single-Field Inflation

In the standard slow-roll inflationary cosmology, quantum fluctuations in a single field, the inflaton, generate approximately Gaussian primordial density perturbations. At present, the bispectrum and trispectrum of the density perturbations have not been observed and the probability distribution for these perturbations is consistent with Gaussianity. However, Planck satellite data will bring a new level of precision to bear on this issue, and it is possible that evidence for non-Gaussian effects in the primordial distribution will be discovered. One possibility is that a trispectrum will be observed without evidence for a non-zero bispectrum. It is not difficult for this to occur in inflationary models where quantum fluctuations in a field other than the inflaton contribute to the density perturbations. A natural question to ask is whether such an observation would rule out the standard scenarios. We explore this issue and find that it is possible to construct single-field models in which inflaton-generated primordial density perturbations have an observable trispectrum, but a bispectrum that is too small to be observed by the Planck satellite. However, an awkward fine tuning seems to be unavoidable.Comment: 15 pages, 3 figures; journal versio

Fab Four: When John and George play gravitation and cosmology

Scalar-tensor theories of gravitation have recently regained a great interest after the discovery of the Chameleon mechanism and of the Galileon models. The former allows, in principle, to reconcile the presence of cosmological scalar fields with the constraints from experiments at the Solar System scale. The latter open up the possibility of building inflationary models that, among other things, do not need ad hoc potentials. Further generalizations have finally led to the most general tensor-scalar theory, recently dubbed the "Fab Four", with only first and second order derivatives of the fields in the equations of motion and that self-tune to a vanishing cosmological constant. This model has a very rich phenomenology that needs to be explored and confronted with experimental data in order to constrain a very large parameter space. In this paper, we present some results regarding a subset of the theory named "John", which corresponds to a non-minimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include a non-minimal, but non-derivative, coupling between scalar field and Ricci scalar, a term named "George" in the Fab Four terminology. In this way, we find a more sensible inflationary model, and, by performing a post-newtonian expansion of spherically symmetric solutions, we derive the set of equations that constrain the parameter space with data from experiments in the solar system.Comment: Minor changes, references added. Version accepted for publication in Advances in Astronom