A non-local theory of massive gravity

We construct a fully covariant theory of massive gravity which does not require the introduction of an external reference metric, and overcomes the usual problems of massive gravity theories (fatal ghosts instabilities, acausality and/or vDVZ discontinuity). The equations of motion of the theory are non-local, but respect causality. The starting point is the quadratic action proposed in the context of the degravitation idea. We show that it is possible to extended it to a fully non-linear covariant theory. This theory describes the five degrees of freedom of a massive graviton plus a scalar ghost. However, contrary to generic non-linear extensions of Fierz-Pauli massive gravity, the ghost has the same mass m as the massive graviton, independently of the background, and smoothly goes into a non-radiative degree of freedom for m-> 0. As a consequence, for $m\sim H_0$ the vacuum instability induced by the ghost is irrelevant even over cosmological time-scales. We finally show that an extension of the model degravitates a vacuum energy density of order $M_{Planck}^4$ down to a value of order $M_{Planck}^2 m^2$, which for $m \sim H_0$ is of order of the observed value of the vacuum energy density.Comment: 45 pages, 2 figs; v2: references and comments added. To appear in PR

Early dark energy from zero-point quantum fluctuations

We examine a cosmological model with a dark energy density of the form $\rho_{DE}(t)=\rho_X(t)+\rho_Z(t)$, where $\rho_X$ is the component that accelerates the Hubble expansion at late times and $\rho_Z(t)$ is an extra contribution proportional to $H^2(t)$. This form of $\rho_Z(t)$ follows from the recent proposal that the contribution of zero-point fluctuations of quantum fields to the total energy density should be computed by subtracting the Minkowski-space result from that computed in the FRW space-time. We discuss theoretical arguments that support this subtraction. By definition, this eliminates the quartic divergence in the vacuum energy density responsible for the cosmological constant problem. We show that the remaining quadratic divergence can be reabsorbed into a redefinition of Newton's constant only under the assumption that the energy-momentum tensor of vacuum fluctuations is conserved in isolation. However, in the presence of an ultra-light scalar field $X$ with $m_X<H_0$, as typical of some dark energy models, the gravity effective action depends both on the gravitational field and on the $X$ field. In this case general covariance only requires the conservation of the total energy-momentum tensor, including both the classical term $T^X_{\mu\nu}$ and the vacuum expectation value of T_{\mu\nu}. If there is an exchange of energy between these two terms, there are potentially observable consequences. We construct an explicit model with an interaction between $\rho_X$ and $\rho_Z$ and we show that the total dark energy density $\rho_{DE}(t)=\rho_X(t)+\rho_Z(t)$ always remains a finite fraction of the critical density at any time, providing a specific model of early dark energy. We discuss the implication of this result for the coincidence problem and we estimate the model parameters by means of a full likelihood analysis using current CMB, SNe Ia and BAO data.Comment: 7 pages, 3 figures; v3: improved discussion, references adde

Zero-point quantum fluctuations in cosmology

We re-examine the classic problem of the renormalization of zero-point quantum fluctuations in a Friedmann-Robertson-Walker background. We discuss a number of issues that arise when regularizing the theory with a momentum-space cutoff, and show explicitly how introducing non-covariant counter-terms allows to obtain covariant results for the renormalized vacuum energy-momentum tensor. We clarify some confusion in the literature concerning the equation of state of vacuum fluctuations. Further, we point out that the general structure of the effective action becomes richer if the theory contains a scalar field phi with mass m smaller than the Hubble parameter H(t). Such an ultra-light particle cannot be integrated out completely to get the effective action. Apart from the volume term and the Einstein-Hilbert term, that are reabsorbed into renormalizations of the cosmological constant and Newton's constant, the effective action in general also has a term proportional to F(phi)R, for some function F(phi). As a result, vacuum fluctuations of ultra-light scalar fields naturally lead to models where the dark energy density has the form rho_{DE}(t)=rho_X(t)+rho_Z(t), where rho_X is the component that accelerates the Hubble expansion at late times and rho_Z(t) is an extra contribution proportional to H^2(t). We perform a detailed comparison of such models with CMB, SNIa and BAO data.Comment: 23 pages, 9 figures. v3: refs added. To appear in Phys. Rev.

Oligorecurrent nodal prostate cancer: radiotherapy quality assurance of the randomized PEACE V-STORM phase II trial.

PURPOSE Aim of this study is to report the results of the radiotherapy quality assurance program of the PEACE V-STORM randomized phase II trial for pelvic nodal oligorecurrent prostate cancer (PCa). MATERIAL AND METHODS A benchmark case (BC) consisting of a postoperative case with 2 nodal recurrences was used for both stereotactic body radiotherapy (SBRT, 30 Gy/3 fx) and whole pelvic radiotherapy (WPRT, 45 Gy/25 fx + SIB boost to 65 Gy). RESULTS BC of 24 centers were analyzed. The overall grading for delineation variation of the 1st BC was rated as 'UV' (Unacceptable Variation) or 'AV' (Acceptable Variation) for 1 and 7 centers for SBRT (33%), and 3 and 8 centers for WPRT (46%), respectively. An inadequate upper limit of the WPRT CTV (n=2), a missing delineation of the prostate bed (n=1), and a missing nodal target volume (n=1 for SBRT and WPRT) constituted the observed 'UV'. With the 2nd BC (n=11), the overall delineation review showed 2 and 8 'AV' for SBRT and WPRT, respectively, with no 'UV'. For the plan review of the 2nd BC, all treatment plans were per protocol for WPRT. SBRT plans showed variability in dose normalization (Median D90% = 30.1 Gy, range 22.9-33.2Gy and 30.6 Gy, range 26.8-34.2Gy for nodes 1 and 2 respectively). CONCLUSIONS Up to 46% of protocol deviations were observed in delineation of WPRT for nodal oligorecurrent PCa, while dosimetric results of SBRT showed the greatest disparities between centers. Repeated BC resulted in an improved adherence to the protocol, translating in an overall acceptable contouring and planning compliance rate among participating centers

Infrared modifications of general relativity and nonlocal massive gravity

Dans cette thèse, nous examinons plusieurs problèmes potentiellement utiles à la compréhension de la nature de l'énergie noire, ce mystérieux composé qui accélère l'expansion cosmique. Après avoir considéré certains aspects techniques relatif au calcul de la densité d'énergie du vide des champs quantiques dans un contexte cosmologique, nous explorerons différents modèles qui modifient la relativité générale dans le régime infrarouge. Ceci sera réalisé soit par l'introduction d'un champ scalaire ultra-léger, en dotant le graviton d'une masse, ou encore en ajoutant des termes non-locaux dans les équations d'Einstein

Bardeen variables and hidden gauge symmetries in linearized massive gravity

We give a detailed discussion of the use of the (3+1) decomposition and of Bardeen's variables in massive gravity linearized over a Minkowski as well as over a de Sitter background. In Minkowski space the Bardeen “potential” Φ, that in the massless case is a nonradiative degree of freedom, becomes radiative and describes the helicity-0 component of the massive graviton. Its dynamics is governed by a simple Klein-Gordon action, supplemented by a term (□Φ)2 if we do not make the Fierz-Pauli tuning of the mass term. In de Sitter the identification of the variable that describes the radiative degree of freedom in the scalar sector is more subtle, and even involves expressions nonlocal in time. The use of this new variable provides a simple and transparent derivation of the Higuchi bound and of the disappearance of the scalar degree of freedom at a special value of m2g/H2. The use of this formalism also allows us to uncover the existence of a hidden gauge symmetry of the massive theory, that becomes manifest only once the nondynamical components of the metric are integrated out, and that is present both in Minkowski and in de Sitter backgrounds

Évaluation de l’acceptabilité, de l’utilité et de l’utilisabilité du tableau de bord du jeu “Programming Game”

Dans le cadre d’un projet de recherche qui porte sur l’usage du jeu pour l’enseignement de la programmation, nous co-concevons un jeu en ligne “Programming Game” et un scénario pédagogique. Le jeu comprend un tableau de bord qui permet à l’enseignant de suivre le travail des élèves et de leur fournir une aide adaptée. Dans cet article, nous présentons les résultats qui portent sur l’évaluation de ce tableau de bord du point de vue de son acceptabilité, utilisabilité et utilité. Les résultats ont été obtenus lors d’expérimentations dans deux classes. Nous concluons par une discussion sur l’usage du tableau de bord par les enseignants

Co-design of a serious game for computing education

The teaching of computer programming will soon become compulsory in the gymnasiums of the canton of Fribourg. To this end, we are conducting a project to co-design a serious game and an associated pedagogical scenario. This project is carried out according to a design-based research (DBR) involving the collaboration of an interdisciplinary group. In this article, which is based on and extends a recent communication, we define the DBR methodology, then analyse the co-design process with the successes and difficulties we encountered. We discuss the factors which facilitated collaboration and ownership of the research by different members of the group