Tentative Appraisal of Compatibility of Small-Scale CMB Anisotropy Detections in the Context of COBE-DMR-Normalized Open and Flat Λ\Lambda CDM Cosmogonies

Goodness-of-fit statistics are used to quantitatively establish the compatibility of CMB anisotropy predictions in a wide range of DMR-normalized, open and spatially-flat $\Lambda$, CDM cosmogonies with the set of all presently available small-scale CMB anisotropy detection data. Conclusions regarding model viability depend sensitively on the prescription used to account for the 1$\sigma$ uncertainty in the assumed value of the DMR normalization, except for low-density, $\Omega_0 \sim 0.3$ -- 0.4, open models which are compatible with the data for all prescriptions used. While large baryon-density (\Omega_B \gap 0.0175 h^{-2}), old (t_0 \gap 15 -- 16 Gyr), low-density ($\Omega_0 \sim 0.2$ -- 0.4), flat-$\Lambda$ models might be incompatible, no model is incompatible with the data for all prescriptions. In fact, some open models seem to fit the data better than should be expected, and this might be an indication that some error bars are mildly overconservative.Comment: 15 page PostScript file, including 6 included figures. Also available via anonymous ftp from ftp://astro.caltech.edu/users/kmg/chi.p

Python I, II, and III CMB Anisotropy Measurement Constraints on Open and Flat-Lambda CDM Cosmogonies

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 Ap

Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach

We extend the pure pseudo-power-spectrum formalism proposed recently in the context of the Cosmic Microwave Background polarized power spectra estimation by Smith (2006) to incorporate cross-spectra computed for multiple maps of the same sky area. We present an implementation of such a technique, paying particular attention to a calculation of the relevant window functions and mixing (mode-coupling) matrices. We discuss the relevance and treatment of the residual $E/B$ leakage for a number of considered sky apodizations as well as compromises and assumptions involved in an optimization of the resulting power spectrum uncertainty. In particular, we investigate the importance of a pixelization scheme, patch geometry, and sky signal priors used in apodization optimization procedures. In addition, we also present results derived for more realistic sky scans as motivated by the proposed balloon borne experiment EBEX. We conclude that the presented formalism thanks to its speed and efficiency can provide an interesting alternative to the CMB polarized power spectra estimators based on the optimal methods at least on angular scales smaller than ~10 degrees. In this regime, we find that it is capable of suppressing the total variance of the estimated $B$-mode spectrum to within a factor of ~2 of the variance due to only the sampling and noise uncertainty of the B-modes alone, as derived from the Fisher matrix approach.Comment: 31 pages, 24 figures, typos corrected on Eq. 32, Appendix C clarified, published in Physical Review

The Measure of Cosmological Parameters

New, large, ground and space telescopes are contributing to an exciting and rapid period of growth in observational cosmology. The subject is now far from its earlier days of being data-starved and unconstrained, and new data are fueling a healthy interplay between observations and experiment and theory. I briefly review here the status of measurements of a number of quantities of interest in cosmology: the Hubble constant, the total mass-energy density, the matter density, the cosmological constant or dark energy component, and the total optical background light.Comment: 12 pages, 4 figures, to be published in "2001: A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics", Michael J. Duff & James T. Liu, eds., (World Scientific, Singapore), in pres

Iterative destriping and photometric calibration for Planck-HFI, polarized, multi-detector map-making

We present an iterative scheme designed to recover calibrated I, Q, and U maps from Planck-HFI data using the orbital dipole due to the satellite motion with respect to the Solar System frame. It combines a map reconstruction, based on a destriping technique, juxtaposed with an absolute calibration algorithm. We evaluate systematic and statistical uncertainties incurred during both these steps with the help of realistic, Planck-like simulations containing CMB, foreground components and instrumental noise, and assess the accuracy of the sky map reconstruction by considering the maps of the residuals and their spectra. In particular, we discuss destriping residuals for polarization sensitive detectors similar to those of Planck-HFI under different noise hypotheses and show that these residuals are negligible (for intensity maps) or smaller than the white noise level (for Q and U Stokes maps), for l > 50. We also demonstrate that the combined level of residuals of this scheme remains comparable to those of the destriping-only case except at very low l where residuals from the calibration appear. For all the considered noise hypotheses, the relative calibration precision is on the order of a few 10e-4, with a systematic bias of the same order of magnitude.Comment: 18 pages, 21 figures. Match published versio

Accelerating Cosmic Microwave Background map-making procedure through preconditioning

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations, and a set of idealised scanning strategies with sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully-optimised standard solvers used today by a factor of as much as 5 in terms of the convergence rate and a factor of up to $4$ in terms of the time to solution, and to do so without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust, and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets.Comment: 19 pages // Final version submitted to A&

ARGO CMB Anisotropy Measurement Constraints on Open and Flat-Lambda CDM Cosmogonies

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 pres

Flat Dark Matter Dominated Models with Hybrid Adiabatic Plus Isocurvature Initial Conditions

We investigate the consequences of flat, dark-matter dominated cosmogonies with hybrid isocurvature and adiabatic initial perturbations and with Harrison-Zel'dovich primordial spectrum normalised to the $COBE$-DMR two-year measurements. We show that whilst the $COBE$-DMR data alone shows no preference for a specific admixture of these modes, acceptable combinations are strongly constrained by other observational data. Nevertheless, in some cases a suitable mixture of these modes still may be used in an attempt to avoid some of the observed problems of purely adiabatic models. Specifically, we consider critical density, cold dark matter (CDM) and mixed dark matter (MDM) models.Comment: Two uuencoded compressed Postscript files containing (1) 19 pages manuscript, (2) four figures (tarred together). Submitted to The Astrophysical Journa

COBE-DMR-normalisation for inflationary flat dark matter models

The two-year COBE-DMR 53 and 90 GHz sky maps, in both galactic and ecliptic coordinates, are used to determine the normalisation of inflationary universe models with a flat global geometry and adiabatic density perturbations. The appropriately normalised cold and mixed dark matter models and cosmological constant dominated, cold dark matter models, computed for a range of values of Omega_b and h, are then compared to various measures of structure in the universe. Critical density CDM models appear to be irreconcilable with observations on both large and small scales simultaneously, whereas MDM models provide a somewhat better fit to the data. Although the COBE-DMR data alone prefer a nearly critical value for the total density, low-density cosmological constant models with Omega_0 greater than or equal to 0.15 can not be rejected at a confidence level exceeding 95%. Such models may also provide a significantly better fit to the matter distribution data than critical density CDM.Comment: uuencoded postscript file (complete text and figures). Accepted for publication in MNRA

CMB EB and TB cross-spectrum estimation via pseudo-spectrum techniques

We discuss methods for estimating EB and TB spectra of the Cosmic Microwave Background anisotropy maps covering limited sky area. Such odd-parity correlations are expected to vanish whenever parity is not broken. As this is indeed the case in the standard cosmologies, any evidence to the contrary would have a profound impact on our theories of the early Universe. Such correlations could also become a sensitive diagnostic of some particularly insidious instrumental systematics. In this work we introduce three different unbiased estimators based on the so-called standard and pure pseudo-spectrum techniques and later assess their performance by means of extensive Monte Carlo simulations performed for different experimental configurations. We find that a hybrid approach combining a pure estimate of B-mode multipoles with a standard one for E-mode (or T) multipoles, leads to the smallest error bars for both EB (or TB respectively) spectra as well as for the three other polarization-related angular power spectra i.e. EE, BB and TE$. However, if both E and B multipoles are estimated using the pure technique the loss of precision for the EB spectrum is not larger than ~30%. Moreover, for the experimental configurations considered here, the statistical uncertainties -- due to sampling variance and instrumental noise -- of the pseudo-spectrum estimates is at most a factor ~1.4 for TT, EE and TE spectra and a factor ~2 for BB, TB and EB spectra, higher than the most optimistic Fisher estimate of the variance.Comment: 23 pages, 10 figures, submitted for publication to Physical Review