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      On the impact of large angle CMB polarization data on cosmological parameters

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          Abstract

          (abridged) We study the impact of the large-angle CMB polarization datasets publicly released by the WMAP and Planck satellites on the estimation of cosmological parameters of the \(\Lambda\)CDM model. To complement large-angle polarization, we consider the high-resolution CMB datasets from either WMAP or Planck, as well as CMB lensing as traced by Planck. In the case of WMAP, we compute the large-angle polarization likelihood starting over from low-resolution frequency maps and their covariance matrices, and perform our own foreground mitigation technique, which includes as a possible alternative Planck 353 GHz data to trace polarized dust. We find that the latter choice induces a downward shift in the optical depth \(\tau\), of order ~\(2\sigma\), robust to the choice of the complementary high-l dataset. When the Planck 353 GHz is consistently used to minimize polarized dust emission, WMAP and Planck 70 GHz large-angle polarization data are in remarkable agreement: by combining them we find \(\tau = 0.066 ^{+0.012}_{-0.013}\), again very stable against the particular choice for high-\(\ell\) data. We find that the amplitude of primordial fluctuations \(A_s\), notoriously degenerate with \(\tau\), is the parameter second most affected by the assumptions on polarized dust removal, but the other parameters are also affected, typically between \(0.5\) and \(1\sigma\). In particular, cleaning dust with \planck's 353 GHz data imposes a \(1\sigma\) downward shift in the value of the Hubble constant \(H_0\), significantly contributing to the tension reported between CMB based and direct measurements of \(H_0\). On the other hand, we find that the appearance of the so-called low \(\ell\) anomaly, a well-known tension between the high- and low-resolution CMB anisotropy amplitude, is not significantly affected by the details of large-angle polarization, or by the particular high-\(\ell\) dataset employed.

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          Cosmological parameters from CMB and other data: a Monte-Carlo approach

          We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.
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            How to measure CMB polarization power spectra without losing information

            We present a method for measuring CMB polarization power spectra given incomplete sky coverage and test it with simulated examples such as Boomerang 2001 and MAP. By augmenting the quadratic estimator method with an additional step, we find that the E and B power spectra can be effectively disentangled on angular scales substantially smaller than the width of the sky patch in the narrowest direction. We find that the basic quadratic and maximum-likelihood methods display a unneccesary sensitivity to systematic errors when T-E cross-correlation is involved, and show how this problem can be eliminated at negligible cost in increased error bars. We also test numerically the widely used approximation that sample variance scales inversely with sky coverage, and find it to be an excellent approximation on scales substantially smaller than the sky patch.
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              Power spectrum estimation from high-resolution maps by Gibbs sampling

              We revisit a recently introduced power spectrum estimation technique based on Gibbs sampling, with the goal of applying it to the high-resolution WMAP data. In order to facilitate this analysis, a number of sophistications have to be introduced, each of which is discussed in detail. We have implemented two independent versions of the algorithm to cross-check the computer codes, and to verify that a particular solution to any given problem does not affect the scientific results. We then apply these programs to simulated data with known properties at intermediate (N_side = 128) and high (N_side = 512) resolutions, to study effects such as incomplete sky coverage and white vs. correlated noise. From these simulations we also establish the Markov chain correlation length as a function of signal-to-noise ratio, and give a few comments on the properties of the correlation matrices involved. Parallelization issues are also discussed, with emphasis on real-world limitations imposed by current super-computer facilities. The scientific results from the analysis of the first-year WMAP data are presented in a companion letter.
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                Author and article information

                Journal
                2016-11-03
                Article
                1611.01123
                ed00bf45-9ada-4b67-bf50-476d22365ffa

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                19 pages, 4 figures, 3 tables
                astro-ph.CO

                Cosmology & Extragalactic astrophysics
                Cosmology & Extragalactic astrophysics

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