On scale-free extensions of massive (bi-)gravity

We discuss a scale-free model of bigravity, in which the mass parameter of the standard bigravity potential is promoted to a dynamical scalar field. This modification retains the ghost-free bigravity structure, in particular it remains free of the Boulware-Deser ghost. We investigate the theory's interaction structure, focusing on its consistent scaling limits and strong coupling scales. Furthermore we explore the model's quadratic action, both around generic background configurations and paying special attention to cosmological backgrounds and to the associated background evolution. Finally we consider the possibility of realizing a phase of late-time acceleration as well as a quasi-de Sitter inflationary stage at early times, when the promoted "mass scalar" becomes the inflaton.Comment: 36 pages; v2 clarifying comments added, references updated, results unchange

Non-local formulation of ghost-free bigravity theory

We study the ghost-free bimetric theory of Hassan and Rosen, with parameters $\beta_i$ such that a flat Minkowski solution exists for both metrics. We show that, expanding around this solution and eliminating one of the two metrics with its own equation of motion, the remaining metric is governed by the Einstein-Hilbert action plus a non-local term proportional to $W_{\mu\nu\rho\sigma} (\Box-m^2)^{-1}W^{\mu\nu\rho\sigma}$, where $W_{\mu\nu\rho\sigma}$ is the Weyl tensor. The result is valid to quadratic order in the metric perturbation and to all orders in the derivative expansion. This example shows, in a simple setting, how such non-local extensions of GR can emerge from an underlying consistent theory, at the purely classical level.Comment: 16 page

La réalité de l’apprentissage par l’échec en entreprise : une approche behavioriste enrichie des émotions

Dans cette recherche, nous envisageons les échecs en matière d’innovation comme des stimuli, susceptibles de déclencher un processus d’apprentissage organisationnel, que nous cherchons à modéliser, à travers l’analyse du lancement raté d’un nouvel espace de vente dans un Grand Magasin français. Ce faisant, nous tentons de comprendre pourquoi une entreprise apprend – ou n’apprend pas – à la suite d’un échec, même si nous refusons d’adopter une approche strictement binaire. Pour atteindre cet objectif, nous inscrivons la question des échecs commerciaux dans le cycle d’apprentissage par l’expérience de March et de ses coauteurs, que nous complétons par l’ajout de deux facteurs : l’engagement affectif et les émotions.In this research, we propose that failure in business can stimulate a process of organizational learning. We seek to model this process, through an analysis of a French department store’s failure to launch a new concept. In doing so, we are attempting to understand why an organization learns – or does not learn – after failing to succeed, even if we refuse to adopt a strict binary approach. To achieve this goal, we reference March and his co-author’s study of learning by experience and we add two factors: affective commitment and emotions.En este estudio, nos planteamos los fracasos en materia de innovación como estímulos, susceptibles de desencadenar un proceso de aprendizaje organizacional, que queremos modelizar, a través del análisis del lanzamiento fracasado de un nuevo espacio de venta en unos Grandes Almacenes franceses. Sin embargo, intentamos comprender porqué una empresa aprende -o no- después de un fracaso, incluso si rechazamos adoptar un enfoque estrictamente binario. Para alcanzar este objetivo, inscribimos la cuestión de los fracasos comerciales en el ciclo de aprendizaje a partir de la experiencia de March y de sus coautores, que completamos con dos factores añadidos: el compromiso afectivo y las emociones

Anisotropy of the astrophysical gravitational wave background: analytic expression of the angular power spectrum and correlation with cosmological observations

Unresolved and resolved sources of gravitational waves are at the origin of a stochastic gravitational wave background. While the computation of its mean density as a function of frequency in a homogeneous and isotropic universe is standard lore, the computation of its anisotropies requires to understand the coarse graining from local systems, to galactic scales and then to cosmology. An expression of the gravitational wave energy density valid in any general spacetime is derived. It is then specialized to a perturbed Friedmann-Lema\^itre spacetime in order to determine the angular power spectrum of this stochastic background as well as its correlation with other cosmological probes, such as the galaxy number counts and weak lensing. Our result for the angular power spectrum also provides an expression for the variance of the gravitational wave background.Comment: 22 pages, 2 figure

Conformal symmetry and nonlinear extensions of nonlocal gravity

We study two nonlinear extensions of the nonlocal $R\,\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\Box^{-2}$ with $(-\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today $w_{\rm DE}\simeq -1.01$, which very closely mimics $\Lambda$CDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordial universe and accelerated expansion in the recent epoch.Comment: 27 pages, 4 figure

Non-local gravity with a Weyl-square term

Recent work has shown that modifications of General Relativity based on the addition to the action of a non-local term $R\,\Box^{-2}R$, or on the addition to the equations of motion of a term involving $(g_{\mu\nu}\Box^{-1} R)$, produce dynamical models of dark energy which are cosmologically viable both at the background level and at the level of cosmological perturbations. We explore a more general class of models based on the addition to the action of terms proportional to $R_{\mu\nu}\,\Box^{-2}R^{\mu\nu}$ and $C_{\mu\nu\rho\sigma}\, \Box^{-2}C^{\mu\nu\rho\sigma}$, where $C_{\mu\nu\rho\sigma}$ is the Weyl tensor. We find that the term $R_{\mu\nu}\,\Box^{-2}R^{\mu\nu}$ does not give a viable background evolution. The non-local Weyl-square term, in contrast, does not contribute to the background evolution but we find that, at the level of cosmological perturbations, it gives instabilities in the tensor sector. Thus, only non-local terms which depend just on the Ricci scalar $R$ appear to be cosmologically viable. We discuss how these results can provide a hint for the mechanism that might generate these effective non-local terms from a fundamental local theory.Comment: 25 pages, 6 figures. v2: the version to appear in PR

Apprendre à écrire et construire des savoirs explicites sur la langue et la communication par l’étude d’un genre textuel: description de pratiques d’enseignants au niveau primaire

Dans cet article, l’auteure décrit des pratiques d’enseignement de l’écriture qui favorisent les liens entre écriture et construction de connaissances ciblées sur un genre spécifique. Une première partie définit le genre textuel comme point d’appui à l’enseignement de l’écriture ainsi qu’à l’articulation entre écriture et apprentissage grammatical. Par la suite, l’auteure présente les caractéristiques méthodologiques d’une recherche doctorale (Marmy Cusin, 2012), centrée sur la pratique d’enseignants au niveau de l’école primaire en Suisse romande mettant en oeuvre une séquence didactique articulant grammaire et texte. La dernière partie de l’article présente quelques résultats extraits de cette recherche : les textes d’auteurs et les textes des élèves sont au coeur des dispositifs mis en oeuvre par les enseignants observés. La notion textuelle travaillée dans la séquence didactique (cohésion des chaines référentielles désignant les personnages d’un récit) n’est pas facile à conceptualiser au niveau primaire et nécessite une médiation importante de la part des enseignants. Enfin, l’enseignement grammatical comme description du fonctionnement de la langue et de la communication est peu visible dans ces pratiques articulées : l’enseignement de l’écriture prend le pas sur l’enseignement de la grammaire. Ce dernier constat laisse à penser que si l’on veut pérenniser les démarches d’analyse descriptive et la construction de connaissances explicites sur la langue et la communication, il est à la fois nécessaire de maintenir un enseignement de la grammaire pour elle-même et viser son intégration à l’action langagière par des dispositifs intégratifs telle la séquence didactique proposée dans cette recherche.In this paper, the author describes practices for the teaching of writing, which enhance the links between writing and knowledge construction centred on a specific text genre. The first part of this paper defines the notion of text genre as a tool for the teaching of writing as well as a way to link the latter with grammar learning. The author goes on to present the methodological characteristics of her doctoral research (Marmy Cusin, 2012), which focuses on teachers’ practices at primary level in French-speaking Switzerland. These teachers experiment a didactic sequence articulating grammar and writing. The last part of the paper presents some of the significant results of this research: authors’ texts and pupils’ texts are at the heart of practices developed by the observed teachers. The textual notion studied here (cohesive relations) is not easy to conceptualize at primary level and requires an important mediation role on the part of the teachers. The teaching of grammar is scarcely visible in these articulated practices: the teaching of writing takes over the teaching of grammar. If one is to develop descriptive analysis procedures and explicit knowledge on language and communication, the author argues therefore that it is both necessary to maintain the teaching of explicit grammar and to integrate it to wider language proficiency through the use of articulated practices such as the didactic sequence proposed in this research