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The cosmic microwave background (CMB) is a significant source of knowledge about the origin and evolution of our universe. However, observations of the CMB are contaminated by foreground emissions, obscuring the CMB signal and reducing its efficacy in constraining cosmological parameters. We employ deep learning as a data-driven approach to CMB cleaning from multi-frequency full-sky maps. In particular, we develop a graph-based Bayesian convolutional neural network based on the U-Net architecture that predicts cleaned CMB with pixel-wise uncertainty estimates. We demonstrate the potential of this technique on realistic simulated data based on the Planck mission. We show that our model accurately recovers the cleaned CMB sky map and resulting angular power spectrum while identifying regions of uncertainty. Finally, we discuss the current challenges and the path forward for deploying our model for CMB recovery on real observations., Comment: Published at the Thirty-fifth Annual Conference on Innovative Applications of Artificial Intelligence (IAAI-23). 7 pages, 6 figures more...

PICO is a concept for a NASA probe-scale mission aiming to detect or constrain the tensor to scalar ratio $r$, a parameter that quantifies the amplitude of inflationary gravity waves. We carry out map-based component separation on simulations with five foreground models and input $r$ values $r_{in}=0$ and $r_{in} = 0.003$. We forecast $r$ determinations using a Gaussian likelihood assuming either no delensing or a residual lensing factor $A_{\rm lens}$ = 27%. By implementing the first full-sky, post component-separation, map-domain delensing, we show that PICO should be able to achieve $A_{\rm lens}$ = 22% - 24%. For four of the five foreground models we find that PICO would be able to set the constraints $r < 1.3 \times 10^{-4} \,\, \mbox{to} \,\, r <2.7 \times 10^{-4}\, (95\%)$ if $r_{in}=0$, the strongest constraints of any foreseeable instrument. For these models, $r=0.003$ is recovered with confidence levels between $18\sigma$ and $27\sigma$. We find weaker, and in some cases significantly biased, upper limits when removing few low or high frequency bands. The fifth model gives a $3\sigma$ detection when $r_{in}=0$ and a $3\sigma$ bias with $r_{in} = 0.003$. However, by correlating $r$ determinations from many small 2.5% sky areas with the mission's 555 GHz data we identify and mitigate the bias. This analysis underscores the importance of large sky coverage. We show that when only low multipoles $\ell \leq 12$ are used, the non-Gaussian shape of the true likelihood gives uncertainties that are on average 30% larger than a Gaussian approximation., Comment: 34 pages, 13 figures, published in JCAP more...

The hot dense environment of the early universe is known to have produced large numbers of baryons, photons, and neutrinos. These extreme conditions may have also produced other long-lived species, including new light particles (such as axions or sterile neutrinos) or gravitational waves. The gravitational effects of any such light relics can be observed through their unique imprint in the cosmic microwave background (CMB), the large-scale structure, and the primordial light element abundances, and are important in determining the initial conditions of the universe. We argue that future cosmological observations, in particular improved maps of the CMB on small angular scales, can be orders of magnitude more sensitive for probing the thermal history of the early universe than current experiments. These observations offer a unique and broad discovery space for new physics in the dark sector and beyond, even when its effects would not be visible in terrestrial experiments or in astrophysical environments. A detection of an excess light relic abundance would be a clear indication of new physics and would provide the first direct information about the universe between the times of reheating and neutrino decoupling one second later., Comment: 5 pages + references; 1 figure; science white paper submitted to the Astro2020 decadal survey more...

Our current understanding of the Universe is established through the pristine measurements of structure in the cosmic microwave background (CMB) and the distribution and shapes of galaxies tracing the large scale structure (LSS) of the Universe. One key ingredient that underlies cosmological observables is that the field that sources the observed structure is assumed to be initially Gaussian with high precision. Nevertheless, a minimal deviation from Gaussianityis perhaps the most robust theoretical prediction of models that explain the observed Universe; itis necessarily present even in the simplest scenarios. In addition, most inflationary models produce far higher levels of non-Gaussianity. Since non-Gaussianity directly probes the dynamics in the early Universe, a detection would present a monumental discovery in cosmology, providing clues about physics at energy scales as high as the GUT scale., Comment: 5 pages + references; Submitted to the Astro2020 call for science white papers. This version: fixed author list more...

The Probe of Inflation and Cosmic Origins (PICO) is an imaging polarimeter that will scan the sky for 5 years in 21 frequency bands spread between 21 and 799 GHz. It will produce full-sky surveys of intensity and polarization with a final combined-map noise level of 0.87 $\mu$K arcmin for the required specifications, equivalent to 3300 Planck missions, and with our current best-estimate would have a noise level of 0.61 $\mu$K arcmin (6400 Planck missions). PICO will either determine the energy scale of inflation by detecting the tensor to scalar ratio at a level $r=5\times 10^{-4}~(5\sigma)$, or will rule out with more than $5\sigma$ all inflation models for which the characteristic scale in the potential is the Planck scale. With LSST's data it could rule out all models of slow-roll inflation. PICO will detect the sum of neutrino masses at $>4\sigma$, constrain the effective number of light particle species with $\Delta N_{\rm eff}<0.06~(2\sigma)$, and elucidate processes affecting the evolution of cosmic structures by measuring the optical depth to reionization with errors limited by cosmic variance and by constraining the evolution of the amplitude of linear fluctuations $\sigma_{8}(z)$ with sub-percent accuracy. Cross-correlating PICO's map of the thermal Sunyaev-Zeldovich effect with LSST's gold sample of galaxies will precisely trace the evolution of thermal pressure with $z$. PICO's maps of the Milky Way will be used to determine the make up of galactic dust and the role of magnetic fields in star formation efficiency. With 21 full sky legacy maps in intensity and polarization, which cannot be obtained in any other way, the mission will enrich many areas of astrophysics. PICO is the only single-platform instrument with the combination of sensitivity, angular resolution, frequency bands, and control of systematic effects that can deliver this compelling, timely, and broad science., Comment: Probe class mission study submitted to NASA and 2020 Decadal Panel. Executive summary: 2.5 pages; Science: 28 pages; Total: 50 pages, 36 figures more...

As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficiently sample from the joint posterior distribution for a multi-component model of the sky with many thousands of correlated physical parameters. The posterior can then be exactly marginalised to estimate properties of the secondary anisotropies, fully taking into account degeneracies with the other signals in the CMB map. We show that this method is computationally tractable using a simple implementation based on the existing Commander component separation code, and also discuss how other types of secondary anisotropy can be accommodated within our framework., Comment: Updated to published version. Sections added on instrumental properties and effects of IR sources more...

We analyse WMAP 7-year temperature data, jointly modeling the cosmic microwave background (CMB) and Galactic foreground emission. We use the Commander code based on Gibbs sampling. Thus, from the WMAP7 data, we derive simultaneously the CMB and Galactic components on scales larger than 1deg with sensitivity improved relative to previous work. We conduct a detailed study of the low-frequency foreground with particular focus on the "microwave haze" emission around the Galactic center. We demonstrate improved performance in quantifying the diffuse galactic emission when Haslam 408MHz data are included together with WMAP7, and the spinning and thermal dust emission is modeled jointly. We also address the question of whether the hypothetical galactic haze can be explained by a spatial variation of the synchrotron spectral index. The excess of emission around the Galactic center appears stable with respect to variations of the foreground model that we study. Our results demonstrate that the new galactic foreground component - the microwave haze - is indeed present., Comment: 16 pages, 16 figures, Published on ApJ more...

We introduce NeedATool (Needlet Analysis Tool), a software for data analysis based on needlets, a wavelet rendition which is powerful for the analysis of fields defined on a sphere. Needlets have been applied successfully to the treatment of astrophysical and cosmological observations, and in particular to the analysis of cosmic microwave background (CMB) data. Usually, such analyses are performed in real space as well as in its dual domain, the harmonic one. Both spaces have advantages and disadvantages: for example, in pixel space it is easier to deal with partial sky coverage and experimental noise; in harmonic domain, beam treatment and comparison with theoretical predictions are more effective. During the last decade, however, wavelets have emerged as a useful tool for CMB data analysis, since they allow to combine most of the advantages of the two spaces, one of the main reasons being their sharp localisation. In this paper, we outline the analytical properties of needlets and discuss the main features of the numerical code, which should be a valuable addition to the CMB analyst's toolbox., Comment: software available at: http://www.fisica.uniroma2.it/~pietrobon/dp_files/dp_NeedATool_download.html more...

We present skeleton studies of non-Gaussianity in the CMB temperature anisotropy observed in the WMAP5 data. The local skeleton is traced on the 2D sphere by cubic spline interpolation which leads to more accurate estimation of the intersection positions between the skeleton and the secondary pixels than conventional linear interpolation. We demonstrate that the skeleton-based estimator of non-Gaussianity of the local type (f_NL) - the departure of the length distribution from the corresponding Gaussian expectation - yields an unbiased and sufficiently converged f_NL-likelihood. We analyse the skeleton statistics in the WMAP5 combined V- and W-band data outside the Galactic base-mask determined from the KQ75 sky-coverage. The results are consistent with Gaussian simulations of the the best-fitting cosmological model, but deviate from the previous results determined using the WMAP1 data. We show that it is unlikely that the improved skeleton tracing method, the omission of Q-band data, the modification of the foreground-template fitting method or the absence of 6 extended regions in the new mask contribute to such a deviation. However, the application of the Kp0 base-mask in data processing does improve the consistency with the WMAP1 results. The f_NL-likelihoods of the data are estimated at 9 different smoothing levels. It is unexpected that the best-fit values show positive correlation with the smoothing scales. Further investigation argues against a point-source or goodness-of-fit explanation but finds that about 30% of either Gaussian or f_NL samples having better goodness-of-fit than the WMAP5 show a similar correlation. We present the estimate f_NL=47.3+/-34.9 (1sigma error) determined from the first four smoothing angles and f_NL=76.8+/-43.1 for the combination of all nine. The former result may be overestimated at the 0.21sigma-level because of point sources., Comment: 17 pages, 14 figures, 5 tables, accepted for publication in MNRAS more...

We study the alignments of the low multipoles of CMB anisotropies with specific directions in the sky (i.e. the dipole, the north Ecliptic pole, the north Galactic pole and the north Super Galactic pole). Performing $10^5$ random extractions we have found that: 1) separately quadrupole and octupole are mildly orthogonal to the dipole but when they are considered together, in analogy to \cite{Copi2006}, we find an unlikely orthogonality at the level of 0.8% C.L.; 2) the multipole vectors associated to $\ell=4$ are unlikely aligned with the dipole at $99.1 %$ C.L.; 3) the multipole vectors associated to $\ell=5$ are mildly orthogonal to the dipole but when we consider only maps that show exactly the same correlation among the multipoles as in the observed WMAP 5yr ILC, these multipole vectors are unlikely orthogonal to the dipole at $99.7 %$ C.L.., Comment: 12 pages, 10 figures, 3 tables. Accepted for publication in JCAP. Few references added and some typos corrected more...

Likelihood analyses of the COBE-DMR sky maps are used to determine the normalization of the inverse-power-law-potential scalar field dark energy model. Predictions of the DMR-normalized model are compared to various observations to constrain the allowed range of model parameters. Although the derived constraints are restrictive, evolving dark energy density scalar field models remain an observationally-viable alternative to the constant cosmological constant model., Comment: 26 pages, 10 figures, ApJ accepted more...

We use joint likelihood analyses of combinations of fifteen cosmic microwave background (CMB) anisotropy data sets from the DMR, UCSB South Pole 1994, Python I--III, ARGO, MAX 4 and 5, White Dish, OVRO, and SuZIE experiments to constrain cosmogonies. We consider open and spatially-flat-Lambda cold dark matter cosmogonies, with nonrelativistic-mass density parameter Omega_0 in the range 0.1--1, baryonic-mass density parameter Omega_B in the range (0.005--0.029) h^{-2}, and age of the universe t_0 in the range (10--20) Gyr. Marginalizing over all parameters but Omega_0, the data favor Omega_0 \simeq 0.9--1 (0.4--0.6) flat-Lambda (open) models. The range in deduced Omega_0 values is partially a consequence of the different combinations of smaller-angular-scale CMB anisotropy data sets used in the analyses, but more significantly a consequence of whether the DMR quadrupole moment is accounted for or ignored in the analysis. For both flat-Lambda and open models, after marginalizing over all other parameters, a lower Omega_B h^2 \simeq 0.005--0.009 is favored. This is also marginally at odds with estimates from more recent CMB anisotropy data and some estimates from standard nucleosynthesis theory and observed light element abundances. For both sets of models a younger universe with t_0 \simeq 12--15 Gyr is favored, consistent with other recent non-CMB indicators. We emphasize that since we consider only a small number of data sets, these results are tentative. More importantly, the analyses here do not rule out the currently favored flat-Lambda model with Omega_0 \sim 0.3, nor the larger Omega_B h^2 values favored by some other data., Comment: 25 pages, 10 figures, submitted to ApJ; the abstract here is slightly abridged more...

We use Owens Valley Radio Observatory (OVRO) cosmic microwave background (CMB) anisotropy data to constrain cosmological parameters. We account for the OVRO beamwidth and calibration uncertainties, as well as the uncertainty induced by the removal of non-CMB foreground contamination. We consider open and spatially-flat-Lambda cold dark matter cosmogonies, with nonrelativistic-mass density parameter Omega_0 in the range 0.1--1, baryonic-mass density parameter Omega_B in the range (0.005--0.029)h^{-2}, and age of the universe t_0 in the range (10--20) Gyr. Marginalizing over all parameters but Omega_0, the OVRO data favors an open (spatially-flat-Lambda) model with Omega_0 ~= 0.33 (0.1). At the 2 sigma confidence level model normalizations deduced from the OVRO data are mostly consistent with those deduced from the DMR, UCSB South Pole 1994, Python I-III, ARGO, MAX 4 and 5, White Dish, and SuZIE data sets., Comment: 14 pages, 3 figures more...

We extend the analysis of Gabor transforms on a Cosmic Microwave Background (CMB) temperature map (Hansen, Gorski and Hivon 2002) to polarisation. We study the temperature and polarisation power spectra on the cut sky, the so-called pseudo power spectra. The transformation kernels relating the full-sky polarisation power spectra and the polarisation pseudo power spectra are found to be similar to the kernel for the temperature power spectrum. This fact is used to construct a fast power spectrum estimation algorithm using the pseudo power spectrum of temperature and polarisation as data vectors in a maximum likelihood approach. Using the pseudo power spectra as input to the likelihood analysis solves the problem of having to invert huge matrices which makes the standard likelihood approach infeasible., Comment: 32 pages, 25 figures, submitted to MNRAS more...

The Fourier transform of a dataset apodised with a window function is known as the Gabor transform. In this paper we extend the Gabor transform formalism to the sphere with the intention of applying it to CMB data analysis. The Gabor coefficients on the sphere known as the pseudo power spectrum is studied for windows of different size. By assuming that the pseudo power spectrum coefficients are Gaussian distributed, we formulate a likelihood ansatz using these as input parameters to estimate the full sky power spectrum from a patch on the sky. Since this likelihood can be calculated quickly without having to invert huge matrices, this allows for fast power spectrum estimation. By using the pseudo power spectrum from several patches on the sky together, the full sky power spectrum can be estimated from full-sky or nearly full-sky observations., Comment: 37 pages, 31 figures, accepted for publication in MNRAS more...

We measure the angular bispectrum of the cosmic microwave background (CMB) radiation anisotropy from the COBE Differential Microwave Radiometer (DMR) four-year sky maps. The angular bispectrum is the harmonic transform of the three-point correlation function, analogous to the angular power spectrum, the harmonic transform of the two-point correlation function. First, we study statistical properties of the bispectrum and the normalized bispectrum. We find the latter more useful for statistical analysis; the distribution of the normalized bispectrum is very much Gaussian, while the bare bispectrum distribution is highly non-Gaussian. Then, we measure 466 modes of the normalized bispectrum, all independent combinations of three-point configurations up to a maximum multipole of 20, the mode corresponding to the DMR beam size. By measuring 10 times as many modes as the sum of previous work, we test Gaussianity of the DMR maps. We compare the data with the simulated Gaussian realizations, finding no significant detection of the normalized bispectrum on the mode-by-mode basis. We also find that the previously reported detection of the normalized bispectrum is consistent with a statistical fluctuation. By fitting a theoretical prediction to the data for the primary CMB bispectrum, which is motivated by slow-roll inflation, we put a weak constraint on a parameter characterizing non-linearity in inflation. Simultaneously fitting the foreground bispectra estimated from interstellar dust and synchrotron template maps shows that neither dust nor synchrotron emissions significantly contribute to the bispectrum at high Galactic latitude. We conclude that the DMR map is consistent with Gaussianity., Comment: 26 pages, 8 figures. submitted to Astrophysical Journal more...

We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No simplifying assumptions are made other than bandlimitation. This reduces typical computation times for convolving the full sky with the asymmetric beam pattern of a megapixel Cosmic Microwave Background (CMB) mission from months to minutes. Our methods enable realistic simulation and careful analysis of data from such missions, taking into account the effects of asymmetric ``point spread functions'' and far side lobes of the physical beam. While motivated by CMB studies, our methods are general and hence applicable to the convolution or filtering of any scalar field on the sphere with an arbitrary, asymmetric kernel. We show in an appendix that the same ideas can be applied to the inverse problems of map-making and beam reconstruction by similarly accelerating the {\em transpose convolution} which is needed for the iterative solution of the normal equations., Comment: 7 pages, 1 figure; results unchanged, minor changes to text. Submitted to Physical Review D more...

As the era of high precision cosmology approaches, the empirically determined power spectrum of the microwave background anisotropy $C_l$ will provide a crucial test for cosmological theories. We present an exact semi-analytic framework for the study of the ampling statistics of the $C_l$ resulting from observations with partial sky coverage and anisotropic noise distributions. This includes space-borne, air-borne and ground-based experiments. We apply this theory to demonstrate its power for constructing fast but unbiased approximate methods for the joint estimation of cosmological parameters. Further applications, such as a test for possible non-Gaussianity of the underlying theory and a ``poor man's power spectrum estimator'' are suggested. An appendix derives recursion relations for the efficient computation of the couplings between spherical harmonics on the cut sky., Comment: Long paper version of astro-ph/9808292 containing detailed calculations, comparison to other methods and discussion. Appendices give explicit formulae for fast recursions used to obtain the results in astro-ph/9808292. Submitted to Physical Review D in January 2000 more...

We apply the Pseudo-C_l formalism to obtain an unbiased, approximate method for efficient simultaneous estimation of several cosmological parameters from large, almost full-sky cosmic microwave background data sets., Comment: 4 pages, 2 colour figures. Talk presented at "Energy Densities in the Universe", XXXVth Rencontres de Moriond, France (January 22-29, 2000) more...

HEALPix is a Hierarchical, Equal Area, and iso-Latitude Pixelisation of the sphere designed to support efficiently - local operations on the pixel set, - a hierarchical tree structure for multi-resolution applications, and - the global Fast Spherical Harmonic transform. The HEALPix concept and the mathematical software based on it introduced in this primer meet the challenges which future high resolution and large volume CMB data sets including the MAP and Planck mission products will present., Comment: This primer is part of the new expanded, improved, and documented version 1.0 of the HEALPix software package, available at http://www.tac.dk/~healpix more...

We use Python I, II, and III cosmic microwave background anisotropy data to constrain cosmogonies. We account for the Python beamwidth and calibration uncertainties. We consider open and spatially-flat-Lambda cold dark matter cosmogonies, with nonrelativistic-mass density parameter Omega_0 in the range 0.1--1, baryonic-mass density parameter Omega_B in the range (0.005--0.029) h^{-2}, and age of the universe t_0 in the range (10--20) Gyr. Marginalizing over all parameters but Omega_0, the combined Python data favors an open (spatially-flat-Lambda) model with Omega_0 simeq 0.2 (0.1). At the 2 sigma confidence level model normalizations deduced from the combined Python data are mostly consistent with those drawn from the DMR, UCSB South Pole 1994, ARGO, MAX 4 and 5, White Dish, and SuZIE data sets., Comment: 20 pages, 7 figures, accepted by ApJ more...

We review our recent claim that there is evidence of non-Gaussianity in the 4 Year COBE DMR data. We present some new results concerning the effect of the galactic cut upon the non-Gaussian signal. These findings imply a localization of the non-Gaussian signal on the Northern galactic hemisphere., Comment: Proceedings of COSMO98 Asilomar more...

We use combinations of ten small-scale cosmic microwave background anisotropy data sets from the UCSB South Pole 1994, ARGO, MAX 4 and 5, White Dish and SuZIE experiments to constrain cosmogonies. We consider open and spatially-flat-Lambda cold dark matter cosmogonies. Marginalizing over all parameters but $\Omega_0$, the combined data favors an Omega_0 simeq 1 for both open and flat-Lambda models. Excluding the smallest angular scale SuZIE data, an Omega_0 simeq 0.3 (1.0) open (flat-Lambda) model is favored. Considering only multi-frequency data with error bars consistent with sample variance and noise considerations, an Omega_0 simeq 0.1 (1) open (flat-Lambda) model is favored. For both open and flat-$\Lambda$ models, after marginalizing over all the other parameters, a lower Omega_B h^2 (sim 0.005) or younger (t_0 sim 10 Gyr) universe is favored. However, the data do not rule out other values of Omega_0 in the flat-Lambda model and other values of Omega_B h^2 in both models. (abriged), Comment: 31 pages, 8 figures, uses aaspp4.sty, accepted by ApJ more...

Much attention has been given to the problem of estimating cosmological parameters from the $C_l$ measured by future experiments. Many of the approaches which are being used either invoke poorly controlled approximations or are computationally expensive. We derive exact results as well as fast and highly accurate approximations for mapping a theoretical model onto the observed power spectrum coefficients and computing their statistical properties. These results obtain from an analytic framework which applies for any azimuthally symmetric sky coverage regardless of the fraction of the sky observed by the experiment., Comment: Typo corrected. 5 pages, 4 figures. To appear in "Evolution of Large Scale Structure", Garching, A. J. Banday et al. (Eds.) (1998). Also available at http://www.tac.dk/~wandelt/downloads.html and http://www.mpa-garching.mpg.de/~cosmo/contributions.html more...

We use data from the ARGO cosmic microwave background (CMB) anisotropy experiment to constrain cosmogonies. We account for the ARGO beamwidth and calibration uncertainties, and marginalize over the offset removed from the data. Our derived amplitudes of the CMB anisotropy detected by the ARGO experiment are smaller than those derived previously. We consider open and spatially-flat-Lambda cold dark matter cosmogonies, with clustered-mass density parameter Omega_0 in the range 0.1-1, baryonic-mass density parameter Omega_B in the range (0.005-0.029)h^{-2}, and age of the universe t_0 in the range (10--20) Gyr. Marginalizing over all parameters but Omega_0, the ARGO data favors an open (spatially-flat-Lambda) model with Omega_0= 0.23 (0.1). However, these numerical values are model dependent. At the 2 sigma confidence level model normalizations deduced from the ARGO data are consistent with those drawn from the UCSB South Pole 1994, MAX 4+5, White Dish, and SuZIE data sets. The ARGO open model normalizations are also consistent with those deduced from the DMR data. However, for most spatially-flat-Lambda models the DMR normalizations are more than 2 sigma above the ARGO ones., Comment: 21 pages of latex. Uses aaspp4.sty. 8 figures included. ApJ in press more...

We introduce and study the distribution of an estimator for the normalized bispectrum of the Cosmic Microwave Background (CMB) anisotropy. We use it to construct a goodness of fit statistic to test the coadded 53 and 90 GHz COBE-DMR 4 year maps for non-Gaussianity. Our results indicate that Gaussianity is ruled out at the confidence level in excess of 98%. This value is a lower bound, given all the investigated systematics. The dominant non-Gaussian contribution is found near the multipole of order $\ell=16$. Our attempts to explain this effect as caused by the diffuse foreground emission from the Galaxy have failed. We conclude that unless there exists a microwave foreground emission which spatially correlates neither with the DIRBE nor Haslam maps, the cosmological CMB anisotropy is genuinely non-Gaussian., Comment: 16 pages, 3 figs uses aasms4.tex, revised and accepted to Ap. J. Lett more...

We present a novel approach to quantifying the morphology of Cosmic Microwave Background (CMB) anisotropy maps. As morphological descriptors, we use shape parameters known as Minkowski functionals. Using the mathematical framework provided by the theory of integral geometry on arbitrary curved supports, we point out the differences to their characterization and interpretation in the case of flat space. With restrictions of real data -- such as pixelization and incomplete sky coverage, to mention just a few -- in mind, we derive and test unbiased estimators for all Minkowski functionals. Various examples, among them the analysis of the four-year COBE DMR data, illustrate the application of our method., Comment: 14 pages, 13 figures, most of which look better in color. Uses AMSTeX, epsf.sty, mncite.sty. Very minor changes to match version accepted for publication in MNRAS more...

Fundamental information about the Universe is encoded in anisotropies of the Cosmic Microwave Background (CMB) radiation. To make full use of this information, an experiment must image the entire sky with the angular resolution, sensitivity, and spectral coverage necessary to reach the limits set by cosmic variance on angular scales >~10'. Recent progress in detector technology allows this to be achieved by a properly designed space mission that fits well within the scope of NASA's Medium-class Explorer program. An essential component of the mission design is an observing strategy that minimizes systematic effects due to instrumental offset drifts. The detector advances make possible a `spin chopping' approach that has significant technical and scientific advantages over the strategy used by COBE, which reconstructed an image of the sky via inversion of a large matrix of differential measurements. The advantages include increased angular resolution, increased sensitivity, and simplicity of instrumentation and spacecraft operations. For the parameters typical of experiments like the Primordial Structures Investigation (PSI) and the Far InfraRed Explorer (FIRE), we show that the spin-chopping strategy produces images of the sky and power spectra of CMB anisotropies that contain no significant systematic artifacts., Comment: 15 pages, including 8 figures. Full resolution and colour versions of simulations and full versions of the preprint available at ftp://omega.jpl.nasa.gov/pub/wwwdir/PSI/papers.htm . Further details of PSI and FIRE are available at http://astrophysics.jpl.nasa.gov/PSI/ and http://caseymac.jpl.nasa.gov/fire/fire.html, respectively more...

We compute the CMB anisotropy in an open inflation CDM model which is normalized to the two-year DMR sky map. Presently available CMB data is consistent with $\Omega_0 \sim 0.3 - 0.4$, but does not strongly disfavour either $\Omega_0 \sim 0.1$ or $\Omega_0 \sim 1$. Accumulating CMB data should strengthen the observational discriminative power, however, a better understanding of systematic effects will be needed before it will be possible to draw robust conclusions about model viability., Comment: 9 pages including 2 figures, one table: two uuencoded postscript files more...

Fourier analysis on a cut sky of the two-year COBE DMR 53 and 90 GHz sky maps (in galactic coordinates) is used to determine the normalisation of an open inflation model based on the cold dark matter scenario. The normalised model is compared to measures of large-scale structure in the universe. Although the DMR data alone does not provide sufficient discriminative power to prefer a particular value of the mass density parameter, the open model appears to be reasonably consistent with observations when Omega_0 ~ 0.3 - 0.4 and merits further study., Comment: uuencoded file containing 6 postscript files (11 pgs text, 4 figures, 1 table) more...

The two-year COBE-DMR 53 and 90 GHz sky maps are used to determine the normalization of inflationary, cosmological constant dominated, cold dark matter models. Although the COBE-DMR data prefer a nearly critical value for the total density, low-density models with Omega_0 > 0.15 can not be rejected at a confidence level > 95%. We compare theoretical predictions for various large scale statistics, computed for a range of values of Omega_0 and h=0.5, or 0.8, to various measures of structure in the universe., Comment: uuencoded file containing 6 postscript files (10 pgs text, 4 figures, 1 table) more...

The two-year COBE-DMR 53 and 90 GHz sky maps in both ecliptic and galactic coordinates, are used to determine the normalisation of inflationary, flat, dark matter dominated universe models. The appropriately normalized cold and mixed dark matter models, computed for a range of values of Omega_baryon and h, and several values of the hot to cold dark matter abundance ratio, are then compared to various measures of structure in the universe., Comment: uuencoded file containing 5 postscript files (11 pgs text, 3 figures, 1 table) more...

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the galactic plane data from the COBE DMR sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g. Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications., Comment: 11 pages, no figures, uuencoded Postscript file. Submitted to ApJ Letters, COBE Preprint #94-07 more...