Non-Gaussianity analysis on local morphological measures of WMAP data

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signal's local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detection is made neither in the orientation analysis nor in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5% at a wavelet scale corresponding to an angular size around 10 degrees, and confirmed at neighbour scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et al. 2004). Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.Comment: 10 pages, 3 figures. Version 2 includes minor changes to match version accepted for publication in MNRA

Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure

Tunable entanglement distillation of spatially correlated down-converted photons

We report on a new technique for entanglement distillation of the bipartite continuous variable state of spatially correlated photons generated in the spontaneous parametric down-conversion process (SPDC), where tunable non-Gaussian operations are implemented and the post-processed entanglement is certified in real-time using a single-photon sensitive electron multiplying CCD (EMCCD) camera. The local operations are performed using non-Gaussian filters modulated into a programmable spatial light modulator and, by using the EMCCD camera for actively recording the probability distributions of the twin-photons, one has fine control of the Schmidt number of the distilled state. We show that even simple non-Gaussian filters can be finely tuned to a ~67% net gain of the initial entanglement generated in the SPDC process.Comment: 12 pages, 6 figure

On the regularity of the covariance matrix of a discretized scalar field on the sphere

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.Comment: 36 pages, 12 figures; minor changes in the text, matches published versio

Exploring two-spin internal linear combinations for the recovery of the CMB polarization

We present a methodology to recover cosmic microwave background (CMB) polarization in which the quantity $P = Q+ iU$ is linearly combined at different frequencies using complex coefficients. This is the most general linear combination of the $Q$ and $U$ Stokes parameters which preserves the physical coherence of the residual contribution on the CMB estimation. The approach is applied to the internal linear combination (ILC) and the internal template fitting (ITF) methodologies. The variance of $P$ of the resulting map is minimized to compute the coefficients of the linear combination. One of the key aspects of this procedure is that it serves to account for a global frequency-dependent shift of the polarization phase. Although in the standard case, in which no global E-B transference depending on frequency is expected in the foreground components, minimizing $\left\langle |P|^2\right\rangle$ is similar to minimizing $\left\langle Q^2\right\rangle$ and $\left\langle U^2\right\rangle$ separately (as previous methodologies proceed), multiplying $Q$ and $U$ by different coefficients induces arbitrary changes in the polarization angle and it does not preserve the coherence between the spinorial components. The approach is tested on simulations, obtaining a similar residual level with respect to the one obtained with other implementations of the ILC, and perceiving the polarization rotation of a toy model with the frequency dependence of the Faraday rotation.Comment: 14 pages, 8 figures, 2 tables. Accepted for publication in MNRA

A low CMB variance in the WMAP data

We have estimated the CMB variance from the three-year WMAP data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fit cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the north ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular we have studied the behaviour of single radiometers and single year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of $n_s$ than the one of the WMAP best-fit model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.Comment: 13 pages, 5 figures. Some new tests added. Section 5 largely modified. Accepted for publication in MNRA

Searching for a dipole modulation in the large-scale structure of the Universe

Several statistical anomalies in the CMB temperature anisotropies seem to defy the assumption of a homogeneous and isotropic universe. In particular, a dipole modulation has been detected both in WMAP and Planck data. We adapt the methodology proposed by Eriksen et al. (2007) on CMB data to galaxy surveys, tracing the large-scale structure. We analyse the NRAO VLA Sky Survey (NVSS) data at a resolution of ~2 degrees for three different flux thresholds: 2.5, 5.0 and 10.0 mJy respectively. No evidence of a dipole modulation is found. This result suggests that the origin of the dipole asymmetry found in the CMB cannot be assigned to secondary anisotropies produced at redshifts around z = 1. However, it could still have been generated at redshifts higher or lower, such as the integrated Sachs-Wolfe effect produced by the local structures. Other all-sky surveys, like the infrared WISE catalogue, could help to explore with a high sensitivity a redshift interval closer than the one probed with NVSS.Comment: 6 pages, 2 figures. Some minor changes have been done from the original manuscript. This paper is accepted by MNRA

Polarized States and Domain Walls in Spinor Bose-Einstein Condensates

We study spin-polarized states and their stability in anti-ferromagnetic states of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including: patterns of the Thomas-Fermi type; structures with a pulse-shape in one component inducing a hole in the other components; states with holes in all three components; and domain walls. A Bogoliubov-de Gennes analysis reveals that families of these states contain intervals of a weak oscillatory instability, except for the domain walls, which are always stable. The development of the instabilities is examined by means of direct numerical simulations.Comment: 7 pages, 9 figures, submitted to Phys. Rev.