Sub-degree CMB anisotropies from inflationary bubbles

It is well known that processes of first order phase transitions may have occurred in the inflationary era. If one or more occurred well before the end of inflation, the nucleated bubbles are stretched to large scales and the primordial power spectrum contains a scale dependent non-Gaussian component provided by the remnants of the bubbles. We predict the anisotropies in the cosmic microwave background (CMB) induced by inflationary bubbles. We build a general analytic model for describing a bubbly perturbation; we evolve each Fourier mode using the linear theory of perturbations from reheating until decoupling; we get the CMB anisotropies by considering the bubbly perturbation intersecting the last scattering surface. The CMB image of an inflationary bubble is a series of concentric isothermal rings of different color (sign of $\delta T/T$) on the scale of the sound horizon at decoupling ($\le 1^{o}$ in the sky); the resulting anisotropy is therefore strongly non-Gaussian. The mean amplitude of $\delta T/T$ for a bubble of size $L$ follows the known estimates for linear perturbations, $\delta T/T\simeq\delta\rho /\rho\cdot (L/H^{-1})^{2}$. In particular, bubbles with size corresponding to the seeds of the observed large scale voids (tens of comoving Mpc) induce an interesting pattern of CMB anisotropies on the sub-degree angular scale, to be further investigated and compared with the forthcoming high resolution CMB maps provided by the MAP and the Planck experiments.Comment: 10 pages, 5 postscript figures, accepted by Ap.

Digital Deblurring of CMB Maps II: Asymmetric Point Spread Function

In this second paper in a series dedicated to developing efficient numerical techniques for the deblurring Cosmic Microwave Background (CMB) maps, we consider the case of asymmetric point spread functions (PSF). Although conceptually this problem is not different from the symmetric case, there are important differences from the computational point of view because it is no longer possible to use some of the efficient numerical techniques that work with symmetric PSFs. We present procedures that permit the use of efficient techniques even when this condition is not met. In particular, two methods are considered: a procedure based on a Kronecker approximation technique that can be implemented with the numerical methods used with symmetric PSFs but that has the limitation of requiring only mildly asymmetric PSFs. The second is a variant of the classic Tikhonov technique that works even with very asymmetric PSFs but that requires discarding the edges of the maps. We provide details for efficient implementations of the algorithms. Their performance is tested on simulated CMB maps.Comment: 9 pages, 13 Figure

Imprints of Primordial Voids on the CMB

We generalize in several ways the results existing in the literature: a) we make use of an exact general relativistic solution for a spherical, nearly empty cavity in the matter dominated era to evaluate the null geodesics and the Sachs-Wolfe effect; b) we evaluate the magnitude of the adiabatic fluctuations of the photon-baryon plasma; c) we study the influence of the shell profile; and d) we take into account the finite thickness of the last scattering surface (LSS) and the influence of its position with respect to the void center. We find empirically an analytic approximation to the Sachs-Wolfe effect for all crossing geometries and we derive an upper limit of $\approx$ 25 $h^{-1}$ Mpc for the comoving radii of voids sitting on the LSS in order to achieve compatibility with COBE's data. As a nearly empty void has an overcomoving expansion of a factor of $\approx$ 4 between decoupling and the present, the maximum allowed size at present is $\approx$ 100 $h^{-1}$ Mpc. On the other hand, the smallness of the comoving size relative to the sound horizon reduces strongly the adiabatic effect by Silk damping and makes it negligible. Most of the signature of primordial voids comes therefore from metric effects and consists of subdegree spots blue or red depending on whether the center lies beyond or within the LSS. In conclusion we refine and confirm earlier constraints on a power law void spectrum originated in an inflationary phase transition and capable of generating the observed large scale structure.Comment: 14 pages, 5 figures, submitted to Montly Notice

Astrophysical and Cosmological Information from Large-scale sub-mm Surveys of Extragalactic Sources

We present a quantitative analysis of the astrophysical and cosmological information that can be extracted from the many important wide-area, shallow surveys that will be carried out in the next few years. Our calculations combine the predictions of the physical model by Granato et al. (2004) for the formation and evolution of spheroidal galaxies with up-to-date phenomenological models for the evolution of starburst and normal late-type galaxies and of radio sources. We compute the expected number counts and the redshift distributions of these source populations separately and then focus on proto-spheroidal galaxies. For the latter objects we predict the counts and redshift distributions of strongly lensed sources at 250, 350, 500, and 850 micron, the angular correlation function of sources detected in the surveys considered, the angular power spectra due to clustering of sources below the detection limit in Herschel and Planck surveys. An optimal survey for selecting strongly lensed proto-spheroidal galaxies is described, and it is shown how they can be easily distinguished from the other source populations. We also discuss the detectability of the imprints of the 1-halo and 2-halo regimes on angular correlation functions and clustering power spectra, as well as the constraints on cosmological parameters that can be obtained from the determinations of these quantities. The novel data relevant to derive the first sub-millimeter estimates of the local luminosity functions of starburst and late-type galaxies, and the constraints on the properties of rare source populations, such as blazars, are also briefly described.Comment: 16 pages, 10 figures. Accepted for publication on MNRA

Polarization Properties of Extragalactic Radio Sources and Their Contribution to Microwave Polarization Fluctuations

We investigate the statistical properties of the polarized emission of extragalactic radio sources and estimate their contribution to the power spectrum of polarization fluctuations in the microwave region. The basic ingredients of our analysis are the NVSS polarization data, the multifrequency study of polarization properties of the B3-VLA sample (Mack et al. 2002) which has allowed us to quantify Faraday depolarization effects, and the 15 GHz survey by Taylor et al. (2001), which has provided strong constraints on the high-frequency spectral indices of sources. The polarization degree of both steep- and flat-spectrum at 1.4 GHz is found to be anti-correlated with the flux density. The median polarization degree at 1.4 GHz of both steep- and flat-spectrum sources brighter than $S(1.4 \hbox{GHz})=80$mJy is $\simeq 2.2$. The data by Mack et al. (2002) indicate a substantial mean Faraday depolarization at 1.4 GHz for steep spectrum sources, while the depolarization is undetermined for most flat/inverted-spectrum sources. Exploiting this complex of information we have estimated the power spectrum of polarization fluctuations due to extragalactic radio sources at microwave frequencies. We confirm that extragalactic sources are expected to be the main contaminant of Cosmic Microwave Background (CMB) polarization maps on small angular scales. At frequencies $< 30$GHz the amplitude of their power spectrum is expected to be comparable to that of the $E$-mode of the CMB. At higher frequencies, however, the CMB dominates.Comment: 10 pages, A&A in pres

A multifrequency angular power spectrum analysis of the Leiden polarization surveys

The Galactic synchrotron emission is expected to be the most relevant source of astrophysical contamination in cosmic microwave background polarization measurements, at least at frequencies 30'. We present a multifrequency analysis of the Leiden surveys, linear polarization surveys covering essentially the Northern Celestial Hemisphere at five frequencies between 408 MHz and 1411 MHz. By implementing specific interpolation methods to deal with these irregularly sampled data, we produced maps of the polarized diffuse Galactic radio emission with pixel size of 0.92 deg. We derived the angular power spectrum (APS) (PI, E, and B modes) of the synchrotron dominated radio emission as function of the multipole, l. We considered the whole covered region and some patches at different Galactic latitudes. By fitting the APS in terms of power laws (C_l = k l^a), we found spectral indices that steepen with increasing frequency: from a = -(1-1.5) at 408 MHz to a = -(2-3) at 1411 MHz for 10 < l < 100 and from a = -0.7 to a = -1.5 for lower multipoles (the exact values depending on the considered sky region and polarization mode). The bulk of this steepening can be interpreted in terms of Faraday depolarization effects. We then considered the APS at various fixed multipoles and its frequency dependence. Using the APSs of the Leiden surveys at 820 MHz and 1411 MHz, we determined possible ranges for the rotation measure, RM, in the simple case of an interstellar medium slab model. Taking also into account the polarization degree at 1.4 GHz, we could break the degeneracy between the identified RM intervals. The most reasonable of them turned out to be RM = 9-17 rad/m^2.Comment: 18 pages, 14 figures. Astronomy and Astrophysics, in pres

Cosmic microwave background: polarization and temperature anisotropies from symmetric structures

I consider the case of anisotropies in the Cosmic Microwave Background (CMB) from one single ordered perturbation source, or seed, existing well before decoupling between matter and radiation. Such structures could have been left by high energy symmetries breaking in the early universe. I focus on the cases of spherical and cylindrical symmetry of the seed. I give general analytic expressions for the polarization and temperature linear perturbations, factoring out of the Fourier integral the dependence on the photon propagation direction and on the geometric coordinates describing the seed. I show how the CMB perturbations manifestly reflect the symmetries of their seeds. CMB anisotropies are obtained with a line of sight integration. This treatment highlights the undulatory properties of the CMB. I show with numerical examples how the polarization and temperature perturbations propagate beyond the size of their seeds, reaching the CMB sound horizon at the time considered. Just like the waves from a pebble thrown in a pond, CMB anisotropy from a seed intersecting the last scattering surface appears as a series of temperature and polarization waves surrounding the seed, extending on the scale of the CMB sound horizon at decoupling, roughly $1^{o}$ in the sky. Each wave is characterized by its own value of the CMB perturbation, with the same mean amplitude of the signal coming from the seed interior. These waves could allow to distinguish relics from high energy processes of the early universe from point-like astrophysical sources, because of their angular extension and amplitude. Also, the marked analogy between polarization and temperature signals offers cross correlation possibilities for the future Planck Surveyor observations.Comment: 21 pages, seven postscript figures, final version accepted for publication in Phys.Rev.

Correlated Component Analysis for diffuse component separation with error estimation on simulated Planck polarization data

We present a data analysis pipeline for CMB polarization experiments, running from multi-frequency maps to the power spectra. We focus mainly on component separation and, for the first time, we work out the covariance matrix accounting for errors associated to the separation itself. This allows us to propagate such errors and evaluate their contributions to the uncertainties on the final products.The pipeline is optimized for intermediate and small scales, but could be easily extended to lower multipoles. We exploit realistic simulations of the sky, tailored for the Planck mission. The component separation is achieved by exploiting the Correlated Component Analysis in the harmonic domain, that we demonstrate to be superior to the real-space application (Bonaldi et al. 2006). We present two techniques to estimate the uncertainties on the spectral parameters of the separated components. The component separation errors are then propagated by means of Monte Carlo simulations to obtain the corresponding contributions to uncertainties on the component maps and on the CMB power spectra. For the Planck polarization case they are found to be subdominant compared to noise.Comment: 17 pages, accepted in MNRA

Quintessence and cosmic acceleration

A cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical quantities depend on the volume scale factor of the Universe, the general solution of the gravitational field equations can be expressed in an exact parametric form. The quintessence field is a free parameter. With an appropriate choice of the scalar field a class of exact solutions is obtained, with an exponential type scalar field potential fixed via the gravitational field equations. The general physical behavior of the model is consistent with the recent cosmological scenario favored by supernova Type Ia observations, indicating an accelerated expansion of the Universe.Comment: 6 pages, 3 figures, to appear in Int. J. Mod. Phys.

Estimating the spectral indices of correlated astrophysical foregrounds by a second-order statistical approach

We present the first tests of a new method, the Correlated Component Analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave Background (CMB). In the present application, the mixing matrix is parameterized in terms of the spectral indices of Galactic synchrotron and thermal dust emissions, while the free-free spectral index is prescribed by basic physics, and is thus assumed to be known. We consider simulated observations of the microwave sky with angular resolution and white stationary noise at the nominal levels for the PLANCK satellite, and realistic foreground emissions, with a position dependent synchrotron spectral index. We work with two sets of PLANCK frequency channels: the low frequency set, from 30 to 143 GHz, complemented with the Haslam 408 MHz map, and the high frequency set, from 217 to 545 GHz. The concentration of intense free-free emission on the Galactic plane introduces a steep dependence of the spectral index of the global Galactic emission with Galactic latitude, close to the Galactic equator. This feature makes difficult for the CCA to recover the synchrotron spectral index in this region, given the limited angular resolution of PLANCK, especially at low frequencies. A cut of a narrow strip around the Galactic equator (|b|<3 deg), however, allows us to overcome this problem. We show that, once this strip is removed, the CCA allows an effective foreground subtraction, with residual uncertainties inducing a minor contribution to errors on the recovered CMB power spectrum.Comment: 9 pages, 5 figures and 1 table accepted by MNRA