The Virtual Element Method with curved edges

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence

The Denoised, Deconvolved, and Decomposed Fermi γ\gamma-ray sky - An application of the D3^3PO algorithm

We analyze the 6.5yr all-sky data from the Fermi LAT restricted to gamma-ray photons with energies between 0.6-307.2GeV. Raw count maps show a superposition of diffuse and point-like emission structures and are subject to shot noise and instrumental artifacts. Using the D3PO inference algorithm, we model the observed photon counts as the sum of a diffuse and a point-like photon flux, convolved with the instrumental beam and subject to Poissonian shot noise. D3PO performs a Bayesian inference in this setting without the use of spatial or spectral templates;i.e., it removes the shot noise, deconvolves the instrumental response, and yields estimates for the two flux components separately. The non-parametric reconstruction uncovers the morphology of the diffuse photon flux up to several hundred GeV. We present an all-sky spectral index map for the diffuse component. We show that the diffuse gamma-ray flux can be described phenomenologically by only two distinct components: a soft component, presumably dominated by hadronic processes, tracing the dense, cold interstellar medium and a hard component, presumably dominated by leptonic interactions, following the hot and dilute medium and outflows such as the Fermi bubbles. A comparison of the soft component with the Galactic dust emission indicates that the dust-to-soft-gamma ratio in the interstellar medium decreases with latitude. The spectrally hard component exists in a thick Galactic disk and tends to flow out of the Galaxy at some locations. Furthermore, we find the angular power spectrum of the diffuse flux to roughly follow a power law with an index of 2.47 on large scales, independent of energy. Our first catalog of source candidates includes 3106 candidates of which we associate 1381(1897) with known sources from the 2nd(3rd) Fermi catalog. We observe gamma-ray emission in the direction of a few galaxy clusters hosting radio halos.Comment: re-submission after referee report (A&A); 17 pages, many colorful figures, 4 tables; bug fixed, flux scale now consistent with Fermi, even lower residual level, pDF -> 1DF source catalog, tentative detection of a few clusters of galaxies, online material http://www.mpa-garching.mpg.de/ift/fermi

The Galaxy in circular polarization: all-sky radio prediction, detection strategy, and the charge of the leptonic cosmic rays

The diffuse Galactic synchrotron emission should exhibit a low level of diffuse circular polarization (CP) due to the circular motions of the emitting relativistic electrons. This probes the Galactic magnetic field in a similar way as the product of total Galactic synchrotron intensity times Faraday depth. We use this to construct an all sky prediction of the so far unexplored Galactic CP from existing measurements. This map can be used to search for this CP signal in low frequency radio data even prior to imaging. If detected as predicted, it would confirm the expectation that relativistic electrons, and not positrons, are responsible for the Galactic radio emission. Furthermore, the strength of real to predicted circular polarization would provide statistical information on magnetic structures along the line-of-sights.Comment: 11 pages, 5 figures, revise

Constraints on Dark Energy state equation with varying pivoting redshift

We assume the DE state equations w(a) = w_0+w_a(a_p-a), and study the dependence of the constraints on w_0 and w_a coefficients on the pivoting redshift 1+z_p=1/a_p. Coefficients are fitted to data including WMAP7, SNIa (Union 2.1), BAO's (including WiggleZ and SDSS results) and H_0 constraints. The fitting algorithm is CosmoMC. We find specific differences between the cases when neutrino mass is allowed or disregarded. More in detail: i) The z_p value yielding uncorrelated constraints on w_0 and w_a is different in the two cases, holding ~0.25 and ~0.35, respectively. (ii) If we consider the intervals allowed to w_0, we find that they shift when z_p increases, in opposite directions for vanishing or allowed neutrino mass. This leads to no overlap between 1sigma intervals already at z_p >~0.4. (iii) The known effect that a more negative state parameter is required to allow for neutrino mass displays its effects on w_a, rather than on w_0. (iv) The w_0-w_a constraints found by using any pivot z_p can be translated into constraints holding at a specific z_p value (0 or the z_p where errors are uncorrelated). When we do so, error ellipses exhibit a satisfactory overlap.Comment: 13 pages, 7 figures, 2 table

Stochastic growth of quantum fluctuations during slow-roll inflation

We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which took place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass $\propto H^2$ (with $H$ as the Hubble parameter) and a massless non-minimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean square gauge invariant inflaton fluctuation grows {\em faster} than any test field with a non-negative effective mass. Hybrid inflationary models can be an exception: the mean square of a test field can dominate over the gauge invariant inflaton fluctuation one on suitably choosing parameters. We also compute the stochastic growth of quantum fluctuation of a second field, relaxing the assumption of its zero homogeneous value, in a generic inflationary model; as a main result, we obtain that the equation of motion of a gauge invariant variable associated, order by order, with a generic quantum scalar fluctuation during inflation can be obtained only if we use the number of e-folds as the time variable in the corresponding Langevin and Fokker-Planck equations for the stochastic approach. We employ this approach to derive some bounds in the case of a model with two massive fields.Comment: 9 pages, 4 figures. Added references, minor changes, matches the version to be published in Phys. Rev.