Spherically Symmetric Solutions in Ghost-Free Massive Gravity

Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz invariant and a Lorentz breaking asymptotically flat behaviour and also fall in two branches. In the first branch, all solutions can be found analitycally and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.Comment: 15 pages. Some change in the reference

Spontaneous Lorentz Breaking and Massive Gravity

We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight difference between gravitons and photons from a common source could be measured.Comment: 4 page

Massive Gravity on a Brane

At present no theory of a massive graviton is known that is consistent with experiments at both long and short distances. The problem is that consistency with long distance experiments requires the graviton mass to be very small. Such a small graviton mass however implies an ultraviolet cutoff for the theory at length scales far larger than the millimeter scale at which gravity has already been measured. In this paper we attempt to construct a model which avoids this problem. We consider a brane world setup in warped AdS spacetime and we investigate the consequences of writing a mass term for the graviton on a the infrared brane where the local cutoff is of order a large (galactic) distance scale. The advantage of this setup is that the low cutoff for physics on the infrared brane does not significantly affect the predictivity of the theory for observers localized on the ultraviolet brane. For such observers the predictions of this theory agree with general relativity at distances smaller than the infrared scale but go over to those of a theory of massive gravity at longer distances. A careful analysis of the graviton two-point function, however, reveals the presence of a ghost in the low energy spectrum. A mode decomposition of the higher dimensional theory reveals that the ghost corresponds to the radion field. We also investigate the theory with a brane localized mass for the graviton on the ultraviolet brane, and show that the physics of this case is similar to that of a conventional four dimensional theory with a massive graviton, but with one important difference: when the infrared brane decouples and the would-be massive graviton gets heavier than the regular Kaluza--Klein modes, it becomes unstable and it has a finite width to decay off the brane into the continuum of Kaluza-Klein states.Comment: 26 pages, LaTeX. v2: extended version with an appendix added about non Fierz-Pauli mass terms. Few typos corrected. Final version appeared in PR

Effect of the irrigation method and genotype on the bioaccumulation of toxic and trace elements in rice

The total concentration of three toxic elements (As, Cd and Pb) and five oligoelements (Cu, Mn, Mo, Ni and Se) has been determined using an original and completely validated ICP-MS method. This was applied to rice grains from 26 different genotypes cultivated in the same soil and irrigated with the same water in three different ways: by the traditional continuous flooding (CF) and by two intermittent methods, the sprinkler irrigation (SP) and the periodical saturation of the soil (SA). The adoption of SP hugely minimizes the average amounts of almost all elements in kernels (−98% for As, −90% for Se and Mn, −60% for Mo, −50% for Cd and Pb), with the only exception of Ni, whose concentration increases the average amount found in the CF rice by 7.5 times. Also SA irrigation is able to reduce the amounts of As, Mo and Pb in kernels but it significantly increases the amounts of Mn, Ni and – mainly - Cd. Also the nature of the genotype determined a wide variability of data within each irrigation method. Genotypes belonging to Indica subspecies are the best bioaccumulators of elements in both CF and SP methods and, never, the worst bioaccumulators for any element/irrigation method combination. In the principal component analysis, PC1 can differentiate samples irrigated by SP by those irrigated by CF and SA, whereas PC2 provides differentiation of CF samples by SA samples. When looking at the loading plot Ni is negatively correlated to the majority of the other elements, except Cu and Cd having negative loadings on PC2. These results allow to envisage that a proper combination of the irrigation method and the nature of rice genotype might be a very valuable tool in order to successfully achieve specific objectives of food safety or the attainment of functional properties

Sorption of ofloxacin and chrysoidine by grape stalk. A representative case of biomass removal of emerging pollutants from wastewater

Emerging pollutants, as antibiotics or dyes, in aquatic ecosystems are a crucial concern and numerous techniques have been developed for their removal. Efficiency, cost effectiveness, and biodegradability reveal biomass sorption as one of the most appealing methods. This study aims to evaluate the effectiveness of grape stalk as a sorbent for ofloxacin (a fluoroquinolone antibiotic) and chrysoidine (an azo-dye). The kinetic and the thermodynamic aspects of the sorption were studied. A pseudo first-order kinetic behavior is shown by both substances, though the kinetic constants of ofloxacin are almost double than those of chrysoidine. The sorption isotherms, which strictly follow the Langmuir model, show remarkable differences as a function of pH and of biomass size. The trend of Langmuir parameters, Qmax and K, as a function of pH and size, is discussed, and different binding mechanisms are proposed. Kinetic and thermodynamic parameters prefigure grape stalk as a potential biomass for scavenging toxic substances from wastewater

Strategic decision-making support for distribution system planning with flexibility alternatives

The ongoing power system transformation requires rethinking the planning and operation practices of the different segments to accommodate the necessary changes and take advantage of the forthcoming opportunities. This paper concerns novel approaches for appraising initiatives involving the use of flexibility from grid-connected users. This paper proposes a Decision Theory based Multi-Criteria Cost-Benefit Analysis (DT-MCA-CBA) methodology for smart grid initiatives that capture the complexity of the distribution system planning activities in which flexibility competes with grid expansion. Based on international guidelines, the proposed DT-MCA-CBA methodology systematically assesses tangible and intangible impacts, considering multiple conflicting criteria. The DT-MCA-CBA methodology relies on a novel approach that combines MCA and Decision Theory to identify the most valuable option in a complex decision-making problem by modelling the stakeholder perspective with the MiniMax regret decision rule. The proposed DT-MCA-CBA methodology is applied to a comparative case study concerning four different approaches for distribution system planning. A web-based software which implements the proposed decision-making framework and the DT-MCA-CBA methodology is developed to provide a novel decision-making support tool for strategical smart distribution system planning

Stability of the Higgs mass in theories with extra dimensions

We analyze the ultraviolet stability of the Higgs mass in recently proposed Kaluza-Klein models compactified on S_1/Z_2 or S_1/(Z_2\times Z_2'), both at the field theory and string theory level. Fayet-Iliopoulos terms of U(1) hypercharge are shown to be of vital importance for this discussion. Models with a single Higgs doublet seem to be generically affected by quadratic divergences.Comment: Contribution to the Proceedings of Durham IPPP meeting May 2001.(12 pages, LaTeX

Wave Function of the Radion in the dS and AdS Brane Worlds

We study the linearized metric perturbation corresponding to the radion for the generalization of the five dimensional two brane setup of Randall and Sundrum to the case when the curvature of each brane is locally constant but non-zero. We find the wave fuction of the radion in a coordinate system where each brane is sitting at a fixed value of the extra coordinate. We find that the radion now has a mass$^2$, which is negative for the case of de Sitter branes but positive for anti de Sitter branes. We also determine the couplings of the radion to matter on the branes, and construct the four dimensional effective theory for the radion valid at low energies. In particular we find that in AdS space the wave function of the radion is always normalizable and hence its effects, though small, remain finite at arbitrarily large brane separations.Comment: Version which appears in Phys. Rev.

Infra-red modification of gravity from asymmetric branes

We consider a single Minkowski brane sandwiched in between two copies of anti-de Sitter space. We allow the bulk Planck mass and cosmological constant to differ on either side of the brane. Linearised perturbations about this background reveal that gravity can be modified in the infra-red. At intermediate scales, the braneworld propagator mimics four-dimensional GR in that it has the correct momentum dependance. However it has the wrong tensor structure. Beyond a source dependant scale, we show that quadratic brane bending contributions become important, and conspire to correct the tensor structure of the propagator. We argue that even higher order terms can consistently be ignored up to very high energies, and suggest that there is no problem with strong coupling. We also consider scalar and vector perturbations in the bulk, checking for scalar ghosts.Comment: Version appearing in CQ

Optical Line Emission from z∼\sim6.8 Sources with Deep Constraints on Lyα\alpha Visibility

We analyze a sample of $z$-dropout galaxies in the CANDELS GOODS South and UDS fields that have been targeted by a dedicated spectroscopic campaign aimed at detecting their Ly$\alpha$ line. Deep IRAC observations at 3.6 and 4.5 $\mu$m are used to determine the strength of optical emission lines affecting these bands at z$\sim$6.5-6.9 in order to i) investigate possible physical differences between Ly$\alpha$ emitting and non-emitting sources; ii) constrain the escape fraction of ionizing photons; iii) provide an estimate of the specific star-formation rate at high redshifts. We find evidence of strong [OIII]+H$\beta$ emission in the average (stacked) SEDs of galaxies both with and without Ly$\alpha$ emission. The blue IRAC [3.6]-[4.5] color of the stack with detected Ly$\alpha$ line can be converted into a rest-frame equivalent width EW([OIII]+H$\beta$)=1500$^{+530}_{-440}\AA$ assuming a flat intrinsic stellar continuum. This strong optical line emission enables a first estimate of f$_{esc}\lesssim$20% on the escape fraction of ionizing photons from Ly$\alpha$ detected objects. The objects with no Ly$\alpha$ line show less extreme EW([OIII]+H$\beta$)=520$^{+170}_{-150}\AA$ suggesting different physical conditions of the HII regions with respect to Ly$\alpha$-emitting ones, or a larger f$_{esc}$. The latter case is consistent with a combined evolution of f$_{esc}$ and the neutral hydrogen fraction as an explanation of the lack of bright Ly$\alpha$ emission at z$>$6. A lower limit on the specific star formation rate, SSFR$>$9.1$Gyr^{-1}$ for $M_{star}=2 \times 10^9 M_{\odot}$ galaxies at these redshifts can be derived from the spectroscopically confirmed sample.Comment: 10 pages, 7 figures; The Astrophysical Journal in press; matched to the published versio