2,337 research outputs found

    Best Unbiased Estimates for the Microwave Background Anisotropies

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    It is likely that the observed distribution of the microwave background temperature over the sky is only one realization of the underlying random process associated with cosmological perturbations of quantum-mechanical origin. If so, one needs to derive the parameters of the random process, as accurately as possible, from the data of a single map. These parameters are of the utmost importance, since our knowledge of them would help us to reconstruct the dynamical evolution of the very early Universe. It appears that the lack of ergodicity of a random process on a 2-sphere does not allow us to do this with arbitrarily high accuracy. We are left with the problem of finding the best unbiased estimators of the participating parameters. A detailed solution to this problem is presented in this article. The theoretical error bars for the best unbiased estimates are derived and discussed.Comment: 26 pages, revtex; minor modifications, 8 new references, to be published in Phys. Rev.

    Estimating parameters of fluctuations in the cosmic microwave background

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    We address questions that arise in statistical analyses of recently detected fluctuations in the Cosmic Microwave Background (CMB). Estimators of the quadrupole amplitude, Q, and spectral index, n, of the CMB angular fluctuation power spectrum are considered. Families of unbiased estimators of Q2 and existence conditions for minimum variance estimators of n are given. We find that the common practice of excluding the quadrupole is not recommended if one is interested in unbiased estimators. We explain previousiy reported correlations of the estimators and show how they depend on the multiple used to normalize the spectrum. We show that a finite beam resolution does not justify the use of truncated least-squares to estimate harmonic coefficients of CMB data

    Cosmological Parameter Estimation: Method

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    CMB anisotropy data could put powerful constraints on theories of the evolution of our Universe. Using the observations of the large number of CMB experiments, many studies have put constraints on cosmological parameters assuming different frameworks. Assuming for example inflationary paradigm, one can compute the confidence intervals on the different components of the energy densities, or the age of the Universe, inferred by the current set of CMB observations. The aim of this note is to present some of the available methods to derive the cosmological parameters with their confidence intervals from the CMB data, as well as some practical issues to investigate large number of parameters

    Prospects for ACT: simulations, power spectrum, and non-Gaussian analysis

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    A new generation of instruments will reveal the microwave sky at high resolution. We focus on one of these, the Atacama Cosmology Telescope, which probes scales 1000<l<10000, where both primary and secondary anisotropies are important. Including lensing, thermal and kinetic Sunyaev-Zeldovich (SZ) effects, and extragalactic point sources, we simulate the telescope's observations of the CMB in three channels, then extract the power spectra of these components in a multifrequency analysis. We present results for various cases, differing in assumed knowledge of the contaminating point sources. We find that both radio and infrared point sources are important, but can be effectively eliminated from the power spectrum given three (or more) channels and a good understanding of their frequency dependence. However, improper treatment of the scatter in the point source frequency dependence relation may introduce a large systematic bias. Even if all thermal SZ and point source effects are eliminated, the kinetic SZ effect remains and corrupts measurements of the primordial slope and amplitude on small scales. We discuss the non-Gaussianity of the one-point probability distribution function as a way to constrain the kinetic SZ effect, and we develop a method for distinguishing this effect from the CMB in a window where they overlap. This method provides an independent constraint on the variance of the CMB in that window and is complementary to the power spectrum analysis.Comment: 22 pages, 11 figures. Submitted to New Astronomy. High resolution figures provided at http://www.princeton.edu/~khuffenb/pubs/prospects-act.htm

    Robust Weak-lensing Mass Calibration of Planck Galaxy Clusters

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    In light of the tension in cosmological constraints reported by the Planck team between their SZ-selected cluster counts and Cosmic Microwave Background (CMB) temperature anisotropies, we compare the Planck cluster mass estimates with robust, weak-lensing mass measurements from the Weighing the Giants (WtG) project. For the 22 clusters in common between the Planck cosmology sample and WtG, we find an overall mass ratio of \left = 0.688 \pm 0.072. Extending the sample to clusters not used in the Planck cosmology analysis yields a consistent value of <MPlanck/MWtG>=0.698±0.062\left< M_{Planck}/M_{\rm WtG} \right> = 0.698 \pm 0.062 from 38 clusters in common. Identifying the weak-lensing masses as proxies for the true cluster mass (on average), these ratios are 1.6σ\sim 1.6\sigma lower than the default mass bias of 0.8 assumed in the Planck cluster analysis. Adopting the WtG weak-lensing-based mass calibration would substantially reduce the tension found between the Planck cluster count cosmology results and those from CMB temperature anisotropies, thereby dispensing of the need for "new physics" such as uncomfortably large neutrino masses (in the context of the measured Planck temperature anisotropies and other data). We also find modest evidence (at 95 per cent confidence) for a mass dependence of the calibration ratio and discuss its potential origin in light of systematic uncertainties in the temperature calibration of the X-ray measurements used to calibrate the Planck cluster masses. Our results exemplify the critical role that robust absolute mass calibration plays in cluster cosmology, and the invaluable role of accurate weak-lensing mass measurements in this regard.Comment: 5 pages, 2 figure

    A needlet ILC analysis of WMAP 9-year polarisation data: CMB polarisation power spectra

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    We estimate Cosmic Microwave Background (CMB) polarisation power spectra, and temperature-polarisation cross-spectra, from the 9-year data of the Wilkinson Microwave Anisotropy Probe (WMAP). Foreground cleaning is implemented using minimum variance linear combinations of the coefficients of needlet decompositions of sky maps for all WMAP channels, to produce maps for CMB temperature anisotropies (T-mode) and polarisation (E-mode and B-mode), for 9 different years of observation. The final power spectra are computed from averages of all possible cross-year power spectra obtained using foreground-cleaned maps for the different years. Our analysis technique yields a measurement of the EE spectrum that is in excellent agreement with theoretical expectations from the current cosmological model. By comparison, the publicly available WMAP EE power spectrum is higher on average (and significantly higher than the predicted EE spectrum from the current best fit) at scales larger than about a degree, an excess that is not confirmed by our analysis.Comment: 13 pages, 7 figures, Significantly changed version accepted for publication in MNRA

    Footprints of Statistical Anisotropies

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    We propose and develop a formalism to describe and constrain statistically anisotropic primordial perturbations. Starting from a decomposition of the primordial power spectrum in spherical harmonics, we find how the temperature fluctuations observed in the CMB sky are directly related to the coefficients in this harmonic expansion. Although the angular power spectrum does not discriminate between statistically isotropic and anisotropic perturbations, it is possible to define analogous quadratic estimators that are direct measures of statistical anisotropy. As a simple illustration of our formalism we test for the existence of a preferred direction in the primordial perturbations using full-sky CMB maps. We do not find significant evidence supporting the existence of a dipole component in the primordial spectrum.Comment: 26 pages, 5 double figures. Uses RevTeX
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