Non-Gaussianities in the local curvature of the 5-year WMAP data

Using the 5 year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the 1 year WMAP data. In Hansen et al 2004, it was found that the northern ecliptic hemisphere was non-Gaussian at the ~1% level testing the densities of hill-, lake and saddle points based on the second derivatives of the CMB temperature map. The 5 year WMAP data has a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limited availability of computer resources, Hansen et al. 2004 were unable to calculate the full covariance matrix for the chi^2 test used. Here we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.Comment: 7 pages, 6 figures, included test on weak lensing simulation

Bayesian analysis of an anisotropic universe model: systematics and polarization

We revisit the anisotropic universe model previously developed by Ackerman, Carroll and Wise (ACW), and generalize both the theoretical and computational framework to include polarization and various forms of systematic effects. We apply our new tools to simulated WMAP data in order to understand the potential impact of asymmetric beams, noise mis-estimation and potential Zodiacal light emission. We find that neither has any significant impact on the results. We next show that the previously reported ACW signal is also present in the 1-year WMAP temperature sky map presented by Liu & Li, where data cuts are more aggressive. Finally, we reanalyze the 5-year WMAP data taking into account a previously neglected (-i)^{l-l'}-term in the signal covariance matrix. We still find a strong detection of a preferred direction in the temperature map. Including multipoles up to l=400, the anisotropy amplitude for the W-band is found to be g = 0.29 +- 0.031, nonzero at 9 sigma. However, the corresponding preferred direction is also shifted very close to the ecliptic poles at (l,b)= (96,30), in agreement with the analysis of Hanson & Lewis, indicating that the signal is aligned along the plane of the solar system. This strongly suggests that the signal is not of cosmological origin, but most likely is a product of an unknown systematic effect. Determining the nature of the systematic effect is of vital importance, as it might affect other cosmological conclusions from the WMAP experiment. Finally, we provide a forecast for the Planck experiment including polarization.Comment: 9 pages, 8 figure

Detection of transplanckian effects in the cosmic microwave background

Quantum gravity effects are expected to modify the primordial density fluctuations produced during inflation and leave their imprint on the cosmic microwave background observed today. We present a new analysis discussing whether these effects are detectable, considering both currently available data and simulated results from an optimal CMB experiment. We find that the WMAP (Wilkinson Microwave Anisotropy Probe) data show no evidence for the particular signature considered in this work but give an upper bound on the parameters of the model. However, a hypothetical experiment shows that with proper data, the trans-Planckian effects should be detectable through alternate sampling methods. This fuzzy conclusion is a result of the nature of the oscillations, since they give rise to a likelihood hypersurface riddled with local maxima. A simple Bayesian analysis shows no significant evidence for the simulated data to prefer a trans-Planckian model. Conventional Markov chain Monte Carlo (MCMC) methods are not suitable for exploring this complicated landscape, but alternative methods are required to solve the problem. This, however, requires extremely high-precision data.Comment: 9 pages, 22 figure

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

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

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

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