The Effect of Asymmetric Beams in the Wilkinson Microwave Anisotropy Probe Experiment

We generate simulations of the cosmic microwave background (CMB) temperature field as observed by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, taking into account the detailed shape of the asymmetric beams and scanning strategy of the experiment, and use these to re-estimate the WMAP beam transfer functions. This method avoids the need of artificially symmetrizing the beams, as done in the baseline WMAP approach, and instead measures the total convolution effect by direct simulation. We find only small differences with respect to the nominal transfer functions, typically less than 1% everywhere, and less than 0.5% at ℓ < 400. The net effect on the CMB power spectrum is less than 0.6%. The effect on all considered cosmological parameters is negligible. For instance, we find that the spectral index of scalar perturbations after taking into account the beam asymmetries is n_s = 0.964 ± 0.014, corresponding to a negative shift of –0.1σ compared to the previously released WMAP results. Our CMB sky simulations are made publicly available and can be used for general studies of asymmetric beam effects in the WMAP data

The effect of asymmetric beams in the Wilkinson Microwave Anisotropy Probe experiment

We generate simulations of the CMB temperature field as observed by the WMAP satellite, taking into account the detailed shape of the asymmetric beams and scanning strategy of the experiment, and use these to re-estimate the WMAP beam transfer functions. This method avoids the need of artificially symmetrizing the beams, as done in the baseline WMAP approach, and instead measures the total convolution effect by direct simulation. We find only small differences with respect to the nominal transfer functions, typically less than 1% everywhere, and less than 0.5% at l<400. The net effect on the CMB power spectrum is less than 0.6%. The effect on all considered cosmological parameters are negligible. For instance, we find that the spectral index of scalar perturbations after taking into account the beam asymmetries is n_s = 0.964 +- 0.014, corresponding to a negative shift of -0.1 sigma compared to the previously released WMAP results. Our CMB sky simulations are made publicly available, and can be used for general studies of asymmetric beam effects in the WMAP data.Comment: 14 pages, 7 figures, published versio

Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this problem. We use this formula and the mark specific cumulative hazard function of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This result leads to necessary and sufficient conditions for consistency of the MLE which imply that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks. Our theoretical results are supported by simulations.Comment: 27 pages, 4 figure

CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.Comment: 10 pages, 7 figures, submitted to Ap

Frequentist comparison of CMB local extrema statistics in the five-year WMAP data with two anisotropic cosmological models

We present local extrema studies of two models that introduce a preferred direction into the observed cosmic microwave background (CMB) temperature field. In particular, we make a frequentist comparison of the one- and two-point statistics for the dipole modulation and ACW models with data from the five-year Wilkinson Microwave Anisotropy Probe (WMAP). This analysis is motivated by previously revealed anomalies in the WMAP data, and particularly the difference in the statistical nature of the temperature anisotropies when analysed in hemispherical partitions. The analysis of the one-point statistics indicates that the previously determined hemispherical variance difficulties can be apparently overcome by a dipole modulation field, but new inconsistencies arise if the mean and the l-dependence of the statistics are considered. The two-point correlation functions of the local extrema, the temperature pair product and the point-point spatial pair-count, demonstrate that the impact of such a modulation is to over-`asymmetrise' the temperature field on smaller scales than the wave-length of the dipole or quadrupole, and this is disfavored by the observed data.The results from the ACW model predictions, however, are consistent with the standard isotropic hypothesis. The two-point analysis confirms that the impact of this type of violation of isotropy on the temperature extrema statistics is relatively weak. From this work, we conclude that a model with more spatial structure than the dipole modulated or rotational-invariance breaking models are required to fully explain the observed large-scale anomalies in the WMAP data.Comment: 10 pages, 4 figures, 3 tables, accepted for publication in MNRA

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies?

(Abridged) A simple six-parameter LCDM model provides a successful fit to WMAP data, both when the data are analyzed alone and in combination with other cosmological data. Even so, it is appropriate to search for any hints of deviations from the now standard model of cosmology, which includes inflation, dark energy, dark matter, baryons, and neutrinos. The cosmological community has subjected the WMAP data to extensive and varied analyses. While there is widespread agreement as to the overall success of the six-parameter LCDM model, various "anomalies" have been reported relative to that model. In this paper we examine potential anomalies and present analyses and assessments of their significance. In most cases we find that claimed anomalies depend on posterior selection of some aspect or subset of the data. Compared with sky simulations based on the best fit model, one can select for low probability features of the WMAP data. Low probability features are expected, but it is not usually straightforward to determine whether any particular low probability feature is the result of the a posteriori selection or of non-standard cosmology. We examine in detail the properties of the power spectrum with respect to the LCDM model. We examine several potential or previously claimed anomalies in the sky maps and power spectra, including cold spots, low quadrupole power, quadropole-octupole alignment, hemispherical or dipole power asymmetry, and quadrupole power asymmetry. We conclude that there is no compelling evidence for deviations from the LCDM model, which is generally an acceptable statistical fit to WMAP and other cosmological data.Comment: 19 pages, 17 figures, also available with higher-res figures on http://lambda.gsfc.nasa.gov; accepted by ApJS; (v2) text as accepte

CMB constraints on noncommutative geometry during inflation

We investigate the primordial power spectrum of the density perturbations based on the assumption that spacetime is noncommutative in the early stage of inflation. Due to the spacetime noncommutativity, the primordial power spectrum can lose rotational invariance. Using the k-inflation model and slow-roll approximation, we show that the deviation from rotational invariance of the primordial power spectrum depends on the size of noncommutative length scale L_s but not on sound speed. We constrain the contributions from the spacetime noncommutativity to the covariance matrix for the harmonic coefficients of the CMB anisotropies using five-year WMAP CMB maps. We find that the upper bound for L_s depends on the product of sound speed and slow-roll parameter. Estimating this product using cosmological parameters from the five-year WMAP results, the upper bound for L_s is estimated to be less than 10^{-27} cm at 99.7% confidence level.Comment: 8 pages, 1 figure, References added, Accepted for publication in EPJC (submitted version

An Estimator for statistical anisotropy from the CMB bispectrum

Various data analyses of the Cosmic Microwave Background (CMB) provide observational hints of statistical isotropy breaking. Some of these features can be studied within the framework of primordial vector fields in inflationary theories which generally display some level of statistical anisotropy both in the power spectrum and in higher-order correlation functions. Motivated by these observations and the recent theoretical developments in the study of primordial vector fields, we develop the formalism necessary to extract statistical anisotropy information from the three-point function of the CMB temperature anisotropy. We employ a simplified vector field model and parametrize the bispectrum of curvature fluctuations in such a way that all the information about statistical anisotropy is encoded in some parameters lambda_{LM} (which measure the anisotropic to the isotropic bispectrum amplitudes). For such a template bispectrum, we compute an optimal estimator for lambda_{LM} and the expected signal-to-noise ratio. We estimate that, for f_{NL} ~ 30, an experiment like Planck can be sensitive to a ratio of the anisotropic to the isotropic amplitudes of the bispectrum as small as 10%. Our results are complementary to the information coming from a power spectrum analysis and particularly relevant for those models where statistical anisotropy turns out to be suppressed in the power spectrum but not negligible in the bispectrum.Comment: 25 pages, LaTeX file. Matches version accepted for publication in JCAP; some references added; Appendix C added to explain the order of the Edgeworth expansion employe

An overview of the current status of CMB observations

In this paper we briefly review the current status of the Cosmic Microwave Background (CMB) observations, summarising the latest results obtained from CMB experiments, both in intensity and polarization, and the constraints imposed on the cosmological parameters. We also present a summary of current and future CMB experiments, with a special focus on the quest for the CMB B-mode polarization.Comment: Latest CMB results have been included. References added. To appear in "Highlights of Spanish Astrophysics V", Proceedings of the VIII Scientific Meeting of the Spanish Astronomical Society (SEA) held in Santander, 7-11 July, 200