Estimation of the angular power spectrum of the Cosmic Microwave Background (CMB) on a small patch of sky is usually plagued by serious spectral leakage, specially when the map has a hard edge. Even on a full sky map, point source masks can alias power from large scales to small scales producing excess variance at high multipoles. We describe a new fast, simple and local method for estimation of power spectra on small patches of the sky that minimizes spectral leakage and reduces the variance of the spectral estimate. For example, when compared with the standard uniform sampling approach on a 8 degree X 8 degree patch of the sky with 2% area masked due to point sources, our estimator halves the errorbars at l=2000 and achieves a more than fourfold reduction in errorbars at l=3500. Thus, a properly analyzed experiment will have errorbars at l=3500 equivalent to those of an experiment analyzed with the now standard technique with ~ 16-25 times the integration time.
Geometric characteristics of random fields are exploited to test the consistency of density perturbation model spectra with COBE data. These CMB maps are analyzed using the number of anisotropy hot spots and their boundary curvature. CMB maps which account for instrumental effects and sky coverage are Monte Carlo generated. These simulations show that a scale invariant Harrison-Zeldovich primordial Gaussian density fluctuation spectrum is consistent with the data. The CMB fluctuation coherence angle, based on boundary curvature, gives a spectral index n = 1.2 +- 0.3.
The identification of non-Gaussian signatures in cosmic microwave background (CMB) temperature maps is one of the main cosmological challenges today. We propose and investigate altenative methods to analyse CMB maps. Using the technique of constrained randomisation we construct surrogate maps which mimic both the power spectrum and the amplitude distribution of simulated CMB maps containing non-Gaussian signals. Analysing the maps with weighted scaling indices and Minkowski functionals yield in both cases statistically significant identification of the primordial non-Gaussianities. We demonstr…
We discuss methods to compute maps of the CMB in models featuring active causal sources and in non-Gaussian models ofinflation. We show our large angle results as well as some preliminary results on small angles. We conclude by discussing on-going work.
The geodesics followed by cosmic microwave background (CMB) photons show different behaviours depending on the geometry of space. Namely, the effect of `mixing geodesics' predicts a distinct signature in CMB maps: threshold-independent elongated anisotropy spots in negatively curved geometries. We have found statistically significant sign for spot elongation in the COBE four year maps. This can be a direct indication for the negative curvature of the Universe.
WMAP has provided CMB maps of the full sky. The raw data is subject to foreground contamination, in particular near to the Galactic plane. Foreground cleaned maps have been derived, e.g., the internal linear combination (ILC) map of Bennett et al. and the reduced foreground TOH map of Tegmark et al. Using S statistics we examine whether residual foreground contamination is left over in the foreground cleaned maps. In particular, we specify which parts of the foreground cleaned maps are sufficiently accurate for the circle-in-the-sky signature. We generalise the S statistic, called D statistic,…
We present a fast, arbitrarily accurate method to simulate the effect of gravitational lensing of the Cosmic Microwave Background anisotropies and polarization fields by large scale structures. We demonstrate the efficiency and accuracy of the method and exhibit their dependence on the algorithm parameters.
We study two different methods to test Gaussianity in CMB maps. One of them is based on the partition function and the other on the morphology of hot and cold spots. The partition function contains information on all the moments and scales, being a useful quantity to compress the large data sets expected from future space missions like Planck. In particular, it contains much richer information than the one available through the radiation power spectrum. The second method utilizes morphological properties of hot and cold spots such as the eccentricity and number of spots in CMB maps. We study t…
We discuss some new problems of the modern cosmology which arose after the BOOMERANG and MAXIMA-1 successful missions. Statistics of high peaks of the CMB anisotropy is analyzed and we discuss possible inner structure of such peaks in the observational data of future MAP and PLANCK missions. We have investigated geometrical and statistical properties of the CMB polarization around such high isolated peaks of anisotropy in the presence of a polarized pixel noise and point sources. The structure of polarization fields in the vicinity of singular points with zero polarization is very sensitive to…
Analysis and denoising of Cosmic Microwave Background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on $12^{\circ}.8\times 12^{\circ}.8$ maps with resolution resembling the experimental one expected for future high resolution space observations. Semianalytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard Cold Dark Matter (CDM) model. Denoising of simulated maps is carried out by removal of wavelet coefficients dominated by instrumental noise. CMB maps with a …
We present in this article two different ways to make CMB maps in practice, from large timelines. One is to make a simple destriping, fitting the data and using the scan intercepts to remove the low frequency noise (stripes). The second, optimal, is to resolve linearly the map-making problem, which in case of big timelines must be simplified and changed from matrices to vectors for the calculations. Assuming few conditions on the noise, it is possible to make fast map-making tools.
A new scheme of sky pixelization is developed for CMB maps. The scheme is based on the Gauss--Legendre polynomials zeros and allows one to create strict orthogonal expansion of the map. A corresponding code has been implemented and comparison with other methods has been done.
Point-source contamination in high-precision Cosmic Microwave Background (CMB) maps severely affects the precision of cosmological parameter estimates. Among the methods that have been proposed for source detection, wavelet techniques based on ``optimal'' filters have been proposed.In this paper we show that these filters are in fact only restrictive cases of a more general class of matched filters that optimize signal-to-noise ratio and that have, in general, better source detection capabilities, especially for lower amplitude sources. These conclusions are confirmed by some numerical experim…
We applay the genus statistics to simulated CMB polarization maps, constructed from the secondary-ionization cosmological models in experimental situations comparable to those of forthcoming space experiments. We find that both the cosmic baryon density and the spectral index of density perturbations are strongly anicorrelated to the reionization redshift. Using the Fisher matrix approach we show that the accuracy on the spectral index and optical depth to the last scattering are improved in the case of genus statistics when comparing with the accuracy obtained from the standard power spectrum…
We consider the 2D wavelet transform with two scales to study sky maps of temperature anisotropies in the cosmic microwave background radiation (CMB). We apply this technique to simulated maps of small sky patches of size 12.8 \times 12.8 square degrees and 1.5' \times 1.5' pixels. The relation to the standard approach, based on the cl's is established through the introduction of the scalogram. We consider temperature fluctuations derived from standard, open and flat-Lambda CDM models. We analyze CMB anisotropies maps plus uncorrelated Gaussian noise (uniform and non-uniform) at idfferent S/N …
A method for ray-tracing through n-body simulations has been recently proposed. It is based on a periodic universe covered by simulation boxes. Photons move along appropriate directions to avoid periodicity effects. Here, an improved version of this method is applied to simulate lensed CMB maps and maps of lens deformations. Particle mesh n-body simulations with appropriate boxes and resolutions are used to evolve the nonlinear inhomogeneities until present time. The resulting maps are statistically analyzed to look for deviations from Gaussianity. These deviations are measured --for the first…
We investigate the non-Gaussian signatures in Cosmic Microwave Background (CMB) maps induced by the intervening large-scale structure through weak lensing. In order to measure the deviation from the Gaussian behavior of the intrinsic temperature anisotropies, we use a family of three morphological descriptors, the so-called Minkowski functionals. We show analytically how these quantities depend on the temperature threshold, and compare the results to numerical experiments including the instrumental effects of Planck. Minkowski functionals can directly measure the statistical properties of the …
The analysis of the CMB anisotropies is a rich source of cosmological informations. In our study, we simulated the signals produced by the relics of a first order phase transition occured during an inflationary epoch in the early Universe. These relics are bubbles of true vacuum that leave a characteristic non-Gaussian imprint on the CMB. We use different statistical estimators in order to evaluate this non-Gaussianity. We obtain some limits on the allowed values of the bubble parameters comparing our results with the experimental data. We also predict the possibility to detect this signal wit…
The arguments presented by Gonzalez-Nuevo et. al (2006) in favour of the Mexican Hat Wavelet Family (MHWF) are critically discussed here. These authors allege the optimal properties of this new class of filters in the detection of point sources embedded in a noise background but their claim is not based upon a solid mathematical foundation and proof.
Gaussianity is the very base for derivation of the cosmological parameters from the CMB angular power spectrum. Non-Gaussian signal, whether originated from experimental error or primordial source, could mimic extra power in the power spectrum, thereby leading to a wrong set of parameters. In this paper we present a new Gaussianity analysis of the derived CMB singals. It is based on the trigonometric moments of phases, which can be concluded with a ``mean angle'', allowing us to see the global trend of non-Gaussianity of the signals. These moments are also closely related to the Pearson's rand…
Weak lensing effects are known to introduce non-linear couplings in CMB temperature maps. In inflationary scenario, the primary CMB anisotropies are expected to form a 2D Gaussian map, for which, the probability distribution function of the ellipticity defined from the local temperature curvature matrix has a very specific shape. I show that lenses alter significantly the shape of this PDF, inducing an excess of elongated structures. The precise functional form is computed for both the field points and the temperature extrema. These analytical results are confirmed by numerical experiments on …
We present the results of a combined analysis of cosmic microwave background (CMB) and X-ray galaxy clusters baryon fraction to deduce constraints over 6 in flationnary cosmological parameters. Such a combination is necessary for breaki ng degeneracies inherent to the CMB.
We have simulated full-sky maps of the Cosmic Microwave Background (CMB) anisotropy expected from Cold Dark Matter (CDM) models at 0.5 and 1.0 degree angular resolution. Statistical properties of the maps are presented as a function of sky coverage, angular resolution, and instrument noise, and the implications of these results for observability of the Doppler peak are discussed. The rms fluctuations in a map are not a particularly robust probe of the existence of a Doppler peak, however, a full correlation analysis can provide reasonable sensitivity. We find that sensitivity to the Doppler pe…
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 method…
We have constructed a full-sky map of the far-infrared suitable for measuring Galactic reddening and extinction (Schlegel, Finkbeiner & Davis 1998: SFD). The SFD map is based upon extensive re-analysis of data from the COBE/DIRBE and IRAS satellite missions. We demonstrate that the maps can correct for extinction problems in the APM galaxy survey. We also determine the most dust-free regions for conducting cosmic microwave background or soft X-ray experiments of extragalactic objects.
We present a method of subtracting the foreground contamination for the measurement of CMB polarization. We calculate the resultant errors on CMB polarization and temperature-polarization cross correlation power spectra for the high frequency instrument (HFI) aboard Planck Surveyor, and estimate the corresponding errors on cosmological parameters.
The analysis of the recent WMAP source catalog shows that the vast majority of bright foreground extragalactic sources detected in CMB maps are Blazars. In this paper we calculate the contamination of CMB anisotropy maps by this type of flat-spectrum, strongly variable and polarized extragalactic radio sources using up-to-date results from recent deep multi-frequency surveys. We found that more than 50 known Blazars (or Blazar candidates) are included in the 90/150 GHz BOOMERANG anisotropy maps, a factor > 15 larger than previously reported. Using a recent derivation of the Blazar radio LogN-L…
The WMAP satellite has made available high quality maps of the sky in five frequency bands ranging from 22 to 94 GHz, with the main scientific objective of studying the anisotropies of the Cosmic Microwave Background (CMB). These maps, however, contain a mixture of emissions from various astrophysical origins, superimposed on CMB emission. The objective of the present work is to make a high resolution CMB map in which contamination by such galactic and extra-galactic foregrounds, as well as by instrumental noise, is as low as possible. The method used is an implementation of a constrained line…
We present a novel method for generation of sets of the Cosmic Microwave Background (CMB) anisotropy maps, which reproduces the $Δł=2$ correlations associated with Alfvén turbulence. The method is based on the non-linear transformation of the CMB maps, which is obtained from the Monte Carlo simulation of the statistically isotropic Gaussian signal. Our method is computationally fast and efficient. We have applied two estimators (the cross-correlation estimator in multipole domain for $ł+1,m$ and $ł-1,m$ modes and circular phase moments) to test the statistical properties of derived maps. Both …
Modelling of the weak lensing of the CMB will be crucial to obtain correct cosmological parameter constraints from forthcoming precision CMB anisotropy observations. The lensing affects the power spectrum as well as inducing non-Gaussianities. We discuss the simulation of full sky CMB maps in the weak lensing approximation and describe a fast numerical code. The series expansion in the deflection angle cannot be used to simulate accurate CMB maps, so a pixel remapping must be used. For parameter estimation accounting for the change in the power spectrum but assuming Gaussianity is sufficient t…
We formulate statistical isotropy of CMB anisotropy maps in its most general form. We also present a fast and orientation independent statistical method to determine deviations from statistical isotropy in CMB polarization maps. Importance of having statistical tests of departures from SI for CMB polarization maps lies not only in interesting theoretical motivations but also in testing cleaned CMB polarization maps for observational artifacts such as residuals from polarized foreground emission. We propose a generalization of the Bipolar Power Spectrum (BiPS) to polarization maps. Application …
I review the general aspects of cosmological parameter estimation from observations of the cosmic microwave background (CMB) temperature anisotropies in the framework of inflationary adiabatic models. The most recent CMB datasets are starting to give good constraints on the relevant parameters of inflationary adiabatic models. They point toward a model consistent with the basic predictions of inflation: a nearly flat universe, with a nearly scale invariant spectrum of primordial fluctuation.
We discuss the tests of nonGaussianity in CMB maps using morphological statistics known as Minkowski functionals. As an example we test degree-scale cosmic microwave background (CMB) anisotropy for Gaussianity by studying the \qmask map that was obtained from combining the QMAP and Saskatoon data. We compute seven morphological functions $M_i(\dt)$, $i=1,...,7$: six \mf and the number of regions $N_c$ at a hundred $\dt$ levels. We also introduce a new parameterization of the morphological functions $M_i(A)$ in terms of the total area $A$ of the excursion set. We show that the latter considerab…
We present a diagnostic test of possible Galactic contamination of cosmic microwave background sky maps designed to provide an independent check on the methods used to compile these maps. The method involves a non-parametric measurement of cross-correlation between the Faraday rotation measure (RM) of extragalactic sources and the measured microwave signal at the same angular position. We argue that statistical properties of the observed distribution of rotation measures are consistent with a Galactic origin, an argument reinforced by a direct measurement of cross-correlation between dust, fre…
The detection of compact sources embedded in a background is a very common problem in many fields of Astronomy. In these lecture notes we present a review of different techniques developed for the detection and extraction of compact sources, with a especial focus on their application to the field of the cosmic microwave background radiation. In particular, we will consider the detection of extragalactic point sources and the thermal and kinematic Sunyaev-Zeldovich effects from clusters of galaxies.
When constraining the primordial non-Gaussianity parameter f_NL with cosmic microwave background anisotropy maps, the bias resulting from the covariance between primordial non-Gaussianity and secondary non-Gaussianities to the estimator of f_NL is generally assumed to be negligible. We show that this assumption may not hold when attempting to measure the primordial non-Gaussianity out to angular scales below a few tens arcminutes with an experiment like Planck, especially if the primordial non-Gaussianity parameter is around the minimum detectability level with f_NL between 5 and 10. In future…
In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of CMB. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel {\em model-independent} method for the estimation of CMB angular power spectrum solely from multi-frequency observations has been proposed and implemented on the first year WMAP data by Saha et al. 2006. All previous estimates of power spectrum of CMB are based upon foreground templates …
We present a fast algorithm for generating full sky, high resolution ($\sim 5'$) simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of $a_{\ell m}$'s and the spectral coefficients $C_\ell$. We show that using an Equidistant Cylindrical Projection of the sky substantially speeds up the calculations. Thus, generating and/or inverting a full sky, high resolution map can be easily achieved with present day computer technology.
One of the main obstacles in extracting the Cosmic Microwave Background (CMB) signal from observations in the mm-submm range is the foreground contamination by emission from galactic components: mainly synchrotron, free-free and thermal dust emission. Due to the statistical nature of the intrinsic CMB signal it is essential to minimize the systematic errors in the CMB temperature determinations. Following the available knowledge of the spectral behavior of the galactic foregrounds simple, power law-like spectra have been assumed. The feasibility of using a simple neural network for extracting …
Observations show that the Cosmic Microwave Background (CMB) contains tiny variations at the 10^{-5} level around its black-body equilibrium temperature. The detection of these temperature fluctuations provides to modern Cosmology evidence for the existence of primordial density perturbations that seeded all the structures presently observed. The vast majority of the cosmological information is contained in the 2-point temperature function, which measures the angular correlation of these temperature fluctuations distributed on the celestial sphere. Here we study such angular correlations using…
High-contrast peaks in the cosmic microwave background (CMB) anisotropy can appear as unresolved sources to observers. We fit simulated CMB maps generated with a cold dark matter model to a set of unresolved features at instrumental resolution 0.5 degrees to 1.5 degrees and present the integral density per steradian n(>|T|) of unresolved features brighter than threshold temperature |T|. A typical medium-scale experiment observing 0.001 sr at 0.5 degree resolution would expect to observe one unresolved feature brighter than 85 \muK after convolution with the beam profile, with less than 5% prob…
We investigate what the lensing information contained in high resolution, low noise CMB temperature maps can teach us about cluster mass profiles. We create lensing fields and Sunyaev-Zel'dovich effect maps from N-body simulations and apply them to primary CMB anisotropies modeled as a Gaussian random field. We examine the success of several techniques of cluster mass reconstruction using CMB lensing information, and make an estimate of the observational requirements necessary to achieve a satisfactory result.
We present an alternative method to analyse cosmic microwave background (CMB) maps. We base our analysis on the study of the partition function. This function is used to examine the CMB maps making use of the different information embedded at different scales and moments. Using the partition function in a likelihood analysis in two dimensions (Q_rms,n), we find the best-fitting model to the best data available at present the COBE--DMR 4 years data set. By means of this analysis we find a maximum in the likelihood function for n=1.8 (-0.65 +0.35) and Q_rms-PS = 10 (-2.5 +3) muK (95 % confidence…
We study the power of several scalar quantities constructed on the sphere (presented in Monteserin et al. 2005) to detect non-Gaussianity on the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractiona…
A new generation of CMB experiments will soon make sensitive high resolution maps of the microwave sky. At angular scales less than $\sim$10 arcminutes, most CMB anisotropies are generated at z $< 1000$, rather than at the surface of last scattering. Therefore, these maps potentially contain an enormous amount of information about the evolution of structure. Whereas spectral information can distinguish the thermal Sunyaev-Zeldovich (tSZ) effect from other anisotropies, the spectral form of anisotropies generated by the gravitational lensing and the kinetic Sunyaev-Zeldovich (kSZ) effects are i…
We explore power spectrum estimation in the context of a Gaussian approximation to the likelihood function. Using the Saskatoon data, we estimate the power averaged through a set of ten filters designed to make the errors on the power estimates uncorrelated. We also present an improvement to using the window function, $W_l$, for calculating bandpower estimates.
We use an iterative generalized least squares map-making algorithm, in conjunction with Monte Carlo techniques, to obtain estimates of the angular power spectrum from cosmic microwave background (CMB) maps. This is achieved by characterizing and removing the instrumental noise contribution in multipole space. This technique produces unbiased estimates and can be applied to an arbitrary experiment. In this paper, we use it on realistic simulations of Planck Low Frequency Instrument (LFI) observations, showing that it can lead to fast and reliable estimation of the CMB angular power spectrum fro…
A major goal of cosmology is to obtain sensitive, high resolution maps of the Cosmic Microwave Background (CMB) anisotropy. Such maps, as would be produced by the recently proposed Microwave Anisotropy Probe (MAP), will contain a wealth of primary information about conditions in the early universe. To mitigate systematic effects when observing the microwave background, it is desirable for the raw data to be collected in differential form: as a set of temperature differences between points in the sky. However, the production of large (mega-pixel) maps from a set of temperature differences is a …
We present a phenomenological investigation of non-Gaussian effects that could be seen on CMB temperature maps. Explicit expressions for the temperature correlation functions are given for different types of primordial mode couplings. We argue that a simplified description of the radial transfer function for the temperature anisotropies allows to get insights into the general properties of the bi and tri-spectra. The accuracy of these results is explored together with the use of the small scale approximation to get explicit expressions of high order spectra. The bi-spectrum is found to have al…
The issue of non-Gaussianity is not only related to distinguishing the theories of the origin of primordial fluctuations, but also crucial for the determination of cosmological parameters in the framework of inflation paradigm. We present an advenced method for testing non-Gaussianity on the whole-sky CMB anisotropies. This method is based on the Kuiper's statistic to probe the two-dimensional uniformity on a periodic mapping square associating phases: return mapping of phases of the derived CMB (similar to auto correlation) and cross correlations between phases of the derived CMB and foregrou…
We have constructed the first all-sky CMB temperature and polarization lensed maps based on a high-resolution cosmological N-body simulation, the Millennium Simulation (MS). We have exploited the lensing potential map obtained using a map-making procedure (Carbone et al. 2008) which integrates along the line-of-sight the MS dark matter distribution by stacking and randomizing the simulation boxes up to $z = 127$, and which semi-analytically supplies the large-scale power in the angular lensing potential that is not correctly sampled by the N-body simulation. The lensed sky has been obtained by…
We have developed a fast, accurate and generally applicable method for inferring the power spectrum and its uncertainties from maps of the cosmic microwave background (CMB) in the presence of inhomogeneous and correlated noise. For maps with 10 to 100 thousand pixels, we apply an exact power spectrum estimation algorithm to submaps of the data at various resolutions, and then combine the results in an optimal manner. To analyze larger maps efficiently one must resort to sub-optimal combinations in which cross-map power spectrum error correlations are only calculated approximately. We expect su…
We estimate the accuracy with which various cosmological parameters can be determined from the CMB temperature and polarization data when various galactic unpolarized and polarized foregrounds are included and marginalized using the multi-frequency Wiener filtering technique. We use the specifications of the future CMB missions MAP and PLANCK for our study. Our results are in qualitative agreement with earlier results obtained without foregrounds, though the errors in most parameters are higher because of degradation of the extraction of polarization signal in the presence of foregrounds.
We describe a sampling method to estimate the polarized CMB signal from observed maps of the sky. We use a Metropolis-within-Gibbs algorithm to estimate the polarized CMB map, containing Q and U Stokes parameters at each pixel, and its covariance matrix. These can be used as inputs for cosmological analyses. The polarized sky signal is parameterized as the sum of three components: CMB, synchrotron emission, and thermal dust emission. The polarized Galactic components are modeled with spatially varying power law spectral indices for the synchrotron, and a fixed power law for the dust, and their…
With the release of the data from the Boomerang and MAXIMA-1 balloon flights, estimates of cosmological parameters based on the Cosmic Microwave Background (CMB) have reached unprecedented precision. In this paper I show that it is possible for these estimates to be substantially biased by features in the primordial density power spectrum. I construct primordial power spectra which mimic to within cosmic variance errors the effect of changing parameters such as the baryon density and neutrino mass, meaning that even an ideal measurement would be unable to resolve the degeneracy. Complementary …
Since the IAU XXIV meeting in 2000, the CMB anisotropy has matured from being one of a number of cosmological probes to forming the bedrock foundation for what is now the standard model of cosmology. The large advances over the past three years have come from making better and better maps of the cosmos. We review the state of measurements of the anisotropy and outline some of what we have learned since 2000. The recent advancements may be placed roughly into three categories: 1) What we learn from the CMB with minimal input from other cosmic measurements such as the Hubble constant; 2) What we…
CMB data analysis is in general done through two main steps : map-making of the time data streams and power spectrum extraction from the maps. The latter basically consists in the separation between the variance of the CMB and that of the noise in the map. Noise must therefore be deeply understood so that the estimation of CMB variance (the power spectrum) is unbiased. I present in this article general techniques to make maps from time streams and to extract the power spectrum from them. We will see that exact, maximum likelihood solutions are in general too slow and hard to deal with to be us…
The statistical properties of a map of the primary fluctuations in the cosmic microwave background (CMB) may be specified to high accuracy by a few thousand power spectra measurements, provided the fluctuations are gaussian, yet the number of parameters relevant for the CMB is probably no more than about 10-20. There is consequently a large degree of redundancy in the power spectrum data. In this paper, we show that the MOPED data compression technique can reduce the CMB power spectrum measurements to about 10-20 numbers (one for each parameter), from which the cosmological parameters can be e…
CMB anisotropy experiments seeking to make maps with more pixels than the 6144 pixels used by the COBE DMR need to address the practical issues of the computer time and storage required to make maps. A simple, repetitive scan pattern reduces these requirements but leaves the experiment vulnerable to systematic errors and striping in the maps. In this paper I give a time-ordered method for map-making with one-horned experiments that has reasonable memory and CPU needs but can handle complex COBE-like scans paths and 1/f noise.
We propose a technique for determination of the spectral parameters of the cosmological signal and pixel noise using observational data on CMB polarization without any additional assumptions. We introduce the notion of so called crossing points in the observational maps and derive the theoretical dependence of the total number of crossing points at different level of the polarization. Finally, we use the statistics of the signal in the vicinities of the singular points, where the polarization of the pure CMB vanishes to correct the final result.
We propose an alternative formalism to simulate CMB temperature maps in $Λ$CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected …
