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Abstract: Magnetic fields appear wherever plasma and currents can be found. As such, they thread through all scales in Nature. It is natural, therefore, to suppose that magnetic fields might have been formed within the high temperature environments of the big bang. Such a primordial magnetic field (PMF) would be expected to arise from and/or influence a variety of cosmological phenomena such as inflation, cosmic phase transitions, big bang nucleosynthesis, the cosmic microwave background (CMB) temperature and polarization anisotropies, the cosmic gravity wave background, and the formation of large-scale structure. In this review, we summarize the development of theoretical models for analyzing the observational consequences of a PMF. We also summarize the current state of the art in the search for observational evidence of a PMF. In particular, we review the framework needed to calculate the effects of a PMF power spectrum on the CMB and the development of large scale structure. We summarize the current constraints on the PMF amplitude and the power spectral index and discuss prospects for better determining these quantities in the near future. [Copyright &y& Elsevier]

We investigate the impact of instrumental systematic errors on the potential of cosmic microwave background polarization experiments targeting primordial B-modes. To do so, we introduce spin-weighted Müller matrix-valued fields describing the linear response of the imperfect optical system and receiver, and give a careful discussion of the behaviour of the induced systematic effects under rotation of the instrument. We give the correspondence between the matrix components and known optical and receiver imperfections, and compare the likely performance of pseudo-correlation receivers and those that modulate the polarization with a half-wave plate. The latter is shown to have the significant advantage of not coupling the total intensity into polarization for perfect optics, but potential effects like optical distortions that may be introduced by the quasi-optical wave plate warrant further investigation. A fast method for tolerancing time-invariant systematic effects is presented, which propagates errors through to power spectra and cosmological parameters. The method extends previous studies to an arbitrary scan strategy, and eliminates the need for time-consuming Monte Carlo simulations in the early phases of instrument and survey design. We illustrate the method with both simple parametrized forms for the systematics and with beams based on physical-optics simulations. Example results are given in the context of next-generation experiments targeting tensor-to-scalar ratios . [ABSTRACT FROM AUTHOR]

We present an application of the fast Independent Component Analysis (fastica) to the Wilkinson Microwave Anisotropy Probe ( WMAP) three-year data with the goal of extracting the cosmic microwave background (CMB) signal. We evaluate the confidence of our results by means of Monte Carlo simulations including the CMB, foreground contaminations and instrumental noise specific to each WMAP frequency band. We perform a complete analysis involving all or a subset of the WMAP channels in order to select the optimal combination for CMB extraction, using the frequency scaling of the reconstructed component as a figure of merit. We find that the combination KQVW provides the best CMB frequency scaling, indicating that the low-frequency foreground contamination in Q, V and W bands is better traced by the emission in the K band. The CMB angular power spectrum is recovered up to the degree scale; it is consistent within errors for all WMAP channel combinations considered, and in close agreement with the WMAP three-year results. A power spectrum analysis is made of the sky map divided into two hemispheres that have been previously reported as showing evidence of an asymmetric ratio of power on large angular scales. We then confirm the findings of several previous works with independent techniques. [ABSTRACT FROM AUTHOR]

Abstract: In the era of high precision CMB measurements, systematic effects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. The effect of non-circular beam on the power spectrum is important at multipoles larger than the beam-width. For recent experiments with high angular resolution, optimal methods of power spectrum estimation are computationally prohibitive and sub-optimal approaches, such as the Pseudo-C l method are used. We provide an analytic framework for correcting the power spectrum for the effect of beam non-circularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. We advocate that when the non-circular beams are important, it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transforms die down fast with m. [Copyright &y& Elsevier]

We consider the shape of the likelihood and posterior surfaces to be used when fitting cosmological models to cosmic microwave background (CMB) temperature and polarization power spectra measured from experiments. In the limit of an all-sky survey with Gaussian-distributed pixel noise we show that the true combined likelihood of the four CMB power spectra (TT, TE, EE and BB) has a Wishart distribution and we discuss the properties of this function. We compare various fits to the posterior surface of the Cl values, both in the case of a single auto-power spectrum and for a combination of temperature and polarization data. In the latter case, it is important that the fits can accurately match the Wishart distribution in the limit of near full-sky coverage. Simple extensions of auto-power spectrum fits to include polarization data generally fail to match correlations between the different power spectra in this limit. Directly fitting pixel values on large scales, as undertaken by the Wilkinson Microwave Anisotropy Probe team in their analysis of the 3-yr data, avoids the complications of characterizing the shape of the posterior for the power spectra. Finally, we demonstrate the importance of the likelihood distribution on analytic marginalization, and provide a formula for analytic marginalization over a calibration error given an all-sky survey. [ABSTRACT FROM AUTHOR]

Small maps of the Rees–Sciama (RS) effect are simulated by using an appropriate N-body code and a certain ray-tracing procedure. A method designed for the statistical analysis of cosmic microwave background (CMB) maps is applied to study the resulting simulations. These techniques, recently proposed – by our team – to consider lens deformations of the CMB, are adapted to deal with the RS effect. This effect and the deviations from Gaussianity associated to it seem to be too small to be detected in the near future. This conclusion follows from our estimation of both the RS angular power spectrum and the RS reduced n-direction correlation functions for . [ABSTRACT FROM AUTHOR]

All-sky thermal and kinetic Sunyaev–Zel'dovich (SZ) maps are presented for assessing how well the Planck mission can find and characterize clusters of galaxies, especially in the presence of primary anisotropies of the cosmic microwave background (CMB) and various Galactic and ecliptic foregrounds. The maps have been constructed from numerical simulations of structure formation in a standard Λ cold dark matter (ΛCDM) cosmology and contain all clusters out to redshifts of with masses exceeding . By construction, the maps properly account for the evolution of cosmic structure, the halo–halo correlation function, the evolving mass function, halo substructure and adiabatic gas physics. The velocities in the kinetic map correspond to the actual density environment at the cluster positions. We characterize the SZ-cluster sample by measuring the distribution of angular sizes, the integrated thermal and kinetic Comptonizations, the source counts in the three relevant Planck channels, and give the angular power spectra of the SZ sky. While our results are broadly consistent with simple estimates based on scaling relations and spherically symmetric cluster models, some significant differences are seen which may affect the number of cluster detectable by Planck. [ABSTRACT FROM AUTHOR]

We present a study of the effect of component separation on the recovered cosmic microwave background (CMB) temperature distribution, considering Gaussian and non-Gaussian input CMB maps. In particular, the non-Gaussian maps have been generated as a mixture of a Gaussian CMB map and a cosmic strings map in different proportions. First, we extract the CMB component from simulated multifrequency Planck data (in small patches of the sky) using the maximum-entropy method (MEM), Wiener filter (WF) and a method based on the subtraction of foreground templates plus a linear combination of frequency channels (LCFC). We then apply a wavelet-based method to study the Gaussianity of the recovered CMB and compare it with the same analysis for the input map. When the original CMB map is Gaussian (and assuming that point sources have been removed), we find that neither MEM nor WF introduce non-Gaussianity in the CMB reconstruction. Regarding the LCFC, the Gaussian character is also preserved provided that the appropriate combination of frequency channels is used. On the contrary, if the input CMB map is non-Gaussian, all the studied methods produce a reconstructed CMB with lower detections of non-Gaussianity than the original map. This effect is mainly due to the presence of instrumental noise in the data, which clearly affects the quality of the reconstructions. In this case, MEM tends to produce slightly higher non-Gaussian detections in the reconstructed map than WF whereas the detections are lower for the LCFC. We have also studied the effect of point sources in the MEM reconstruction. If no attempt to remove point sources is performed, they clearly contaminate the CMB reconstruction, introducing spurious non-Gaussianity. When the brightest point sources are removed from the data using the Mexican Hat Wavelet, the Gaussian character of the CMB is preserved. However, when analysing larger regions of the sky, the variance of our estimators will be appreciably reduced and, in this case, we expect the point source residuals to introduce spurious non-Gaussianity in the CMB distribution. Therefore, a careful subtraction (or masking) of point source emission is crucial in order to be able to perform Gaussian analysis of the CMB. [ABSTRACT FROM AUTHOR]

We perform a blind multicomponent analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP) 1-yr foreground-cleaned maps using Spectral Matching Independent Component Analysis ( smica). We provide a new estimate of the cosmic microwave background (CMB) power spectrum as well as the amplitude of the CMB anisotropies across frequency channels. We show that the CMB anisotropies are compatible with temperature fluctuations as expected from the standard paradigm. The analysis also allows us to identify and separate a weak residual Galactic emission, present significantly in the Q band outside of the Kp2 1 mask limits, and mainly concentrated at low Galactic latitudes. We produce a map of this residual component by Wiener filtering using estimated parameters. The level of contamination of CMB data by this component is compatible with the WMAP-team estimation of foreground residual contamination. In addition, the multicomponent analysis allows us to estimate jointly the power spectrum of unresolved point-source emission. [ABSTRACT FROM AUTHOR]

The recent observations of cross temperature–polarization power spectra of the cosmic microwave background (CMB) made by the Wilkinson Microwave Anisotropy Probe ( WMAP) satellite are in better agreement with a high value of the Thomson scattering optical depth τ≈ 0.17. This value is close to τ= 0.3, which is taken as the upper limit in the parameter extraction analysis made by the WMAP team. However, models with τ∼ 0.3 provide a good fit to current CMB data and are not significantly excluded when combined with large-scale structure data. By making use of a self-consistent reionization model, we verify the astrophysical feasibility of models with τ∼ 0.3. It turns out that current data on various observations related to the thermal and ionization history of the intergalactic medium are not able to rule out τ∼ 0.3. The possibility of a very extended reionization epoch can significantly undermine the WMAP constraints on crucial cosmological parameters such as the Hubble constant, the spectral index of primordial fluctuations and the amplitude of dark matter clustering. [ABSTRACT FROM AUTHOR]

We develop the pseudo- Cℓ method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo- Cℓ covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo- Cℓ values to the underlying all-sky Cℓ values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cℓ from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from to . We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo- Cℓ power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered. [ABSTRACT FROM AUTHOR]

Quadratic methods with heuristic weighting (e.g. pseudo-or correlation function methods) represent an efficient way to estimate power spectra of the cosmic microwave background (CMB) anisotropies and their polarization. We construct the sample covariance properties of such estimators for CMB polarization, and develop semi-analytic techniques to approximate the pseudo-sample covariance matrices at high Legendre multipoles, taking account of the geometric effects of mode coupling and the mixing between the electric (E) and magnetic (B) polarization that arise for observations covering only part of the sky. TheE– Bmixing ultimately limits the applicability of heuristically weighted quadratic methods to searches for the gravitational-wave signal in the large-angleB-mode polarization, even for methods that can recover (exactly) unbiased estimates of theB-mode power. We show that for surveys covering 1 or 2 per cent of the sky, the contribution ofE-mode power to the covariance of the recoveredB-mode power spectrum typically limits the tensor-to-scalar ratio that can be probed with such methods to∼0.05. [ABSTRACT FROM AUTHOR]

A detailed search has been made for evidence of residual foreground contributions to the cosmic microwave background (CMB) in the map generated by theWilkinson Microwave Anisotropy Probe(WMAP), a map that has been (nominally) cleaned for the foreground already. We find positive results in that various features relate to Galactic properties. For example, on the largest angular scales we find significant differences between the power in the fluctuations for positive and negative Galactic latitudes and between the four Galactic quadrants. There are also differences between the power spectrum at latitudes within 10° of the plane and at higher latitudes. The mean temperature shows similar variations. An explanation in terms of Galactic effects seems inescapable.In an effort to find the origin of these Galactic-style effects we have examined evidence from Galactic gamma-rays, specifically from the EGRET instrument. We are mindful that the CMB maps examined have already been‘cleaned’ (for CR and other effects) in a rather complex way, but, in our view, the cleaning has left some potentially serious‘contaminations’. A correlation is found between gamma-ray intensities and the CMB and other CR indicators. For example, regions of the Galaxy having (line-of-sight) steep CR energy spectra have low mean CMB temperatures, and the important Loop I edge region, where the CR intensity is high, has a high mean temperature.Most of the large-scale Galactic asymmetries (e.g. north–south difference and quadrant variations) have analogues in CR asymmetries and also in some other Galactic properties, such as the column density of gas. Thus, it is possible to hypothesize about direct CR-induced contributions, although it may be that CRs are simply the indicators of Galactic‘conditions’ which are influencing the residual CMB fluctuations.Irrespective of the actual cause of the correlations we have endeavoured to extrapolate to the situation where the residual foreground is minimized. The effect on the usually derived cosmological properties is briefly examined. The least that can be said is that the‘error’ in some of these properties has been underestimated. [ABSTRACT FROM AUTHOR]

We describe the source subtraction strategy and observations for the extended Very Small Array (VSA), a cosmic microwave background interferometer operating at 33 GHz. A total of 453 sources were monitored at 33 GHz using a dedicated source subtraction baseline. 131 sources brighter than 20 mJy were directly subtracted from the VSA visibility data. Some characteristics of the subtracted sources, such as spectra and variability, are discussed. The 33-GHz source counts are estimated from a sample selected at 15 GHz. The selection of VSA fields in order to avoid bright sources introduces a bias into the observed counts. This bias is corrected and the resulting source count is estimated to be complete in the flux-density range 20–114 mJy. The 33-GHz source counts are used to calculate a correction to the VSA power spectrum for sources below the subtraction limit. [ABSTRACT FROM AUTHOR]

Polarized diffuse emission observations at 2.3 GHz in a high Galactic latitude area are presented. The field, centred at , is located in the region observed by the BOOMERanG experiment. Our observations were carried out with the Parkes radio telescope, and represent the highest frequency detection to date in a low-emission area. Because of the weaker Faraday rotation effect, the high frequency allows an estimate of the Galactic synchrotron contamination of the cosmic microwave background polarization (CMBP) which is more reliable than that achieved at 1.4 GHz. We find that the angular power spectra of the E- and B-modes have slopes of and , indicating a flattening with respect to 1.4 GHz. Extrapolated up to 32 GHz, the E-mode spectrum is about three orders of magnitude lower than that of the CMBP, allowing a clean detection even at this frequency. The best improvement concerns the B-mode, for which our single-dish observations provide the first estimate of the contamination on angular scales close to the CMBP peak (about 2°). We find that the CMBP B-mode should be stronger than the synchrotron contamination at 90 GHz for models with tensor-to-scalar perturbation ratio . This low level could move down to 60–70 GHz the optimal window for CMBP measurements. [ABSTRACT FROM AUTHOR]

We presentXspect, a method to obtain estimates of the angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies including analytical error bars developed for theArcheopsexperiment. Cross-power spectra are computed from a set of maps and each of them is in itself an unbiased estimate of the power spectrum as long as the detector noises are uncorrelated. Then, the cross-power spectra are combined into a final temperature power spectrum with error bars analytically derived from the cross-correlation matrix.This method presents three main useful properties: (1) no estimation of the noise power spectrum is needed; (2) complex weighting schemes including sky covering and map noise properties can be easily taken into account, and corrected for, for each input map; and (3) error bars are quickly computed analytically from the data themselves with no Monte Carlo simulations involved.Xspectalso permits the study of common fluctuations between maps from different sky surveys such as CMB, Sunyaev–Zel'dovich effect or mass fluctuations from weak lensing observations. [ABSTRACT FROM AUTHOR]

Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates forPlanck-like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. AssumingPlanck-like low-frequency noise, the noise power spectrum is accurately white at high multipoles. Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis ofPlanckdata and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic‘1/ f’ noise. [ABSTRACT FROM AUTHOR]

Precision measurements of the Sunyaev–Zel'dovich (SZ) effect in upcoming blank sky surveys require theoretical understanding of all physical processes with ≳10 per cent effects on the SZ power spectrum. We show that the observed cluster magnetic field could reduce the SZ power spectrum by ∼20 per cent at , where the SZ power spectrum will be precisely measured by the Sunyaev–Zel'dovich array (SZA) and the Atacama Cosmology Telescope (ACT). At smaller scale, this effect is larger and could reach a factor of several. Such an effect must be considered for an unbiased interpretation of the SZ data. Although the magnetic effect on the SZ power spectrum is very similar to that of radiative cooling, it is measurable by multiband cosmic microwave background polarization measurement. [ABSTRACT FROM AUTHOR]

A combined analysis of cosmic microwave background (CMB) and Lyman α forest data can constrain the matter power spectrum from small scales of about all the way to the horizon scale. The long lever arm and complementarity provided by such an analysis have previously led to a significant tightening of the constraints on the shape and the amplitude of the power spectrum of primordial density fluctuations. We present here a combined analysis of the WMAP three-year results with Lyman α forest data. The amplitude of the matter power spectrum σ8 and the spectral index ns inferred from the joint analysis of high- and low-resolution Lyman α forest data as analysed by Viel & Haehnelt are consistent with the new WMAP results to within 1σ. The joint analysis with the mainly low-resolution data as analysed by McDonald et al. suggests a value of σ8 that is ∼2σ higher than that inferred from the WMAP three-year data alone. The joint analysis of the three-year WMAP and the Lyman α forest data also does not favour a running of the spectral index. The best-fitting values for a combined analysis of the three-year WMAP data, other CMB data, 2-degree Field (2dF) data and the Lyman α forest data are . [ABSTRACT FROM AUTHOR]