Revised WMAP constraints on neutrino masses and other extensions of the minimal Λ\LambdaCDM model

Recently, two issues concerning the three-year WMAP likelihood code were pointed out. On large angular scales ($l \lesssim 30$), a sub-optimal likelihood approximation resulted in a small power excess. On small angular scales ($l \gtrsim 300$), over-subtraction of unresolved point sources produced a small power deficit. For a minimal six-parameter cosmological model, these two effects conspired to decrease the value of $n_s$ by $\sim 0.7 \sigma$. In this paper, we study the change in preferred parameter ranges for more extensive cosmological models, including running of $n_s$, massive neutrinos, curvature, and the equation of state for dark energy. We also include large-scale structure and supernova data in our analysis. We find that the parameter ranges for $\alpha_s$, $\Omega_k$ and $w$ are not much altered by the modified analysis. For massive neutrinos the upper limit on the sum of the neutrino masses decreases from $M_\nu < 1.90$eV to $M_\nu < 1.57$eV when using the modified WMAP code and WMAP data only. We also find that the shift of $n_s$ to higher values is quite robust to these extensions of the minimal cosmological model.Comment: 7 pages. Matching version published in Physical Review D. Figures changed, references added, additional comment

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

Cosmological Parameters from CMB Maps without Likelihood Approximation

We propose an efficient Bayesian MCMC algorithm for estimating cosmological parameters from CMB data without use of likelihood approximations. It builds on a previously developed Gibbs sampling framework that allows for exploration of the joint CMB sky signal and power spectrum posterior, P(s,Cl|d), and addresses a long-standing problem of efficient parameter estimation simultaneously in high and low signal-to-noise regimes. To achieve this, our new algorithm introduces a joint Markov Chain move in which both the signal map and power spectrum are synchronously modified, by rescaling the map according to the proposed power spectrum before evaluating the Metropolis-Hastings accept probability. Such a move was already introduced by Jewell et al. (2009), who used it to explore low signal-to-noise posteriors. However, they also found that the same algorithm is inefficient in the high signal-to-noise regime, since a brute-force rescaling operation does not account for phase information. This problem is mitigated in the new algorithm by subtracting the Wiener filter mean field from the proposed map prior to rescaling, leaving high signal-to-noise information invariant in the joint step, and effectively only rescaling the low signal-to-noise component. To explore the full posterior, the new joint move is then interleaved with a standard conditional Gibbs sky map move. We apply our new algorithm to simplified simulations for which we can evaluate the exact posterior to study both its accuracy and performance, and find good agreement with the exact posterior; marginal means agree to less than 0.006 sigma, and standard deviations to better than 3%. The Markov Chain correlation length is of the same order of magnitude as those obtained by other standard samplers in the field.Comment: 9 pages, 3 figures, Published in Ap

Large-Scale Polarized Foreground Component Separation for Planck

We use Bayesian component estimation methods to examine the prospects for large-scale polarized map and cosmological parameter estimation with simulated Planck data assuming simplified white noise properties. The sky signal is parametrized as the sum of the CMB, synchrotron emission, and thermal dust emission. The synchrotron and dust components are modelled as power-laws, with a spatially varying spectral index for synchrotron and a uniform index for dust. Using the Gibbs sampling technique, we estimate the linear polarisation Q and U posterior amplitudes of the CMB, synchrotron and dust maps as well as the two spectral indices in ~4 degree pixels. We use the recovered CMB map and its covariance in an exact pixel likelihood algorithm to estimate the optical depth to reionization tau, the tensor-to-scalar ratio r, and to construct conditional likelihood slices for the EE and BB spectra. Given our foreground model, we find sigma(tau)~0.004 for tau=0.1, sigma(r)~0.03 for a model with r=0.1, and a 95% upper limit of r<0.02 for r=0.0.Comment: 15 pages, 12 figures, submitted to MNRA

Impact on the tensor-to-scalar ratio of incorrect Galactic foreground modelling

A key goal of many Cosmic Microwave Background experiments is the detection of gravitational waves, through their B-mode polarization signal at large scales. To extract such a signal requires modelling contamination from the Galaxy. Using the Planck experiment as an example, we investigate the impact of incorrectly modelling foregrounds on estimates of the polarized CMB, quantified by the bias in tensor-to-scalar ratio r, and optical depth tau. We use a Bayesian parameter estimation method to estimate the CMB, synchrotron, and thermal dust components from simulated observations spanning 30-353 GHz, starting from a model that fits the simulated data, returning r<0.03 at 95% confidence for an r=0 model, and r=0.09+-0.03 for an r=0.1 model. We then introduce a set of mismatches between the simulated data and assumed model. Including a curvature of the synchrotron spectral index with frequency, but assuming a power-law model, can bias r high by ~1-sigma (delta r ~ 0.03). A similar bias is seen for thermal dust with a modified black-body frequency dependence, incorrectly modelled as a power-law. If too much freedom is allowed in the model, for example fitting for spectral indices in 3 degree pixels over the sky with physically reasonable priors, we find r can be biased up to ~3-sigma high by effectively setting the indices to the wrong values. Increasing the signal-to-noise ratio by reducing parameters, or adding additional foreground data, reduces the bias. We also find that neglecting a 1% polarized free-free or spinning dust component has a negligible effect on r. These tests highlight the importance of modelling the foregrounds in a way that allows for sufficient complexity, while minimizing the number of free parameters.Comment: 11 pages, 7 figures, submitted to MNRA

Analysis of WMAP 7-year Temperature Data: Astrophysics of the Galactic Haze

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 Ap