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Register a new userEstimating the Power Spectrum of the Cosmic Microwave Background
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J. R. Bond CITA
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We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same C_ls. The quadratic estimator can also be used to directly determine cosmological parameters and their uncertainties. While the two methods both require O(N^3) operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to O(N^2) thus making it practical for forthcoming megapixel datasets.
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We present a determination by the Archeops experiment of the angular power spectrum of the cosmic microwave background anisotropy in 16 bins over the multipole range l=15-350. Archeops was conceived as a precursor of the Planck HFI instrument by using the same optical design and the same technology for the detectors and their cooling. Archeops is a balloon-borne instrument consisting of a 1.5 m aperture diameter telescope and an array of 21 photometers maintained at ~100 mK that are operating in 4 frequency bands centered at 143, 217, 353 and 545 GHz. The data were taken during the Arctic night of February 7, 2002 after the instrument was launched by CNES from Esrange base (Sweden). The entire data cover ~ 30% of the sky.This first analysis was obtained with a small subset of the dataset using the most sensitive photometer in each CMB band (143 and 217 GHz) and 12.6% of the sky at galactic latitudes above 30 degrees where the foreground contamination is measured to be negligible. The large sky coverage and medium resolution (better than 15 arcminutes) provide for the first time a high signal-to-noise ratio determination of the power spectrum over angular scales that include both the first acoustic peak and scales probed by COBE/DMR. With a binning of Delta(l)=7 to 25 the error bars are dominated by sample variance for l below 200. A companion paper details the cosmological implications.
We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and a principal component analysis technique. The primordial power spectrum is decomposed into a dominant scale-invariant Gaussian adiabatic component plus a series of orthonormal modes whose detailed form only depends the noise model for a particular CMB experiment. However, in general these modes are localised across wavenumbers with 0.01 < k < 0.2 Mpc^-1, displaying rapid oscillations on scales corresponding the acoustic peaks where the sensitivity to primordial power spectrum is greatest. The performance of this method is assessed using simulated data for the Planck satellite, and the full cosmological plus power spectrum parameter space is integrated out using Markov Chain Monte Carlo. As a proof of concept we apply this data compression technique to the current CMB data from WMAP, ACBAR, CBI and VSA. We find no evidence for the breaking of scale-invariance from measurements of four PCA mode amplitudes, which is translated to a constraint on the scalar spectral index n_S(k_0=0.04 Mpc^-1)=0.94+-0.04 in accordance with WMAP studies.
We present measurements of anisotropy in the Cosmic Microwave Background (CMB) from the first season of observations with the Degree Angular Scale Interferometer (DASI). The instrument was deployed at the South Pole in the austral summer 1999--2000, and made observations throughout the following austral winter. We have measured the angular power spectrum of the CMB in the range 100<l<900 with high signal-to-noise. In this paper we review the formalism used in the analysis, in particular the use of constraint matrices to project out contaminants such as ground and point source signals, and to test for correlations with diffuse foreground templates. We find no evidence of foregrounds other than point sources in the data, and find a maximum likelihood temperature spectral index beta = -0.1 +/- 0.2 (1 sigma), consistent with CMB. We detect a first peak in the power spectrum at l approx 200, in agreement with previous experiments. In addition, we detect a peak in the power spectrum at l approx 550 and power of similar magnitude at l approx 800 which are consistent with the second and third harmonic peaks predicted by adiabatic inflationary cosmological models.
Gravitational lensing due to the large-scale distribution of matter in the cosmos distorts the primordial Cosmic Microwave Background (CMB) and thereby induces new, small-scale $B$-mode polarization. This signal carries detailed information about the distribution of all the gravitating matter between the observer and CMB last scattering surface. We report the first direct evidence for polarization lensing based on purely CMB information, from using the four-point correlations of even- and odd-parity $E$- and $B$-mode polarization mapped over $sim30$ square degrees of the sky measured by the POLARBEAR experiment. These data were analyzed using a blind analysis framework and checked for spurious systematic contamination using null tests and simulations. Evidence for the signal of polarization lensing and lensing $B$-modes is found at 4.2$sigma$ (stat.+sys.) significance. The amplitude of matter fluctuations is measured with a precision of $27%$, and is found to be consistent with the Lambda Cold Dark Matter ($Lambda$CDM) cosmological model. This measurement demonstrates a new technique, capable of mapping all gravitating matter in the Universe, sensitive to the sum of neutrino masses, and essential for cleaning the lensing $B$-mode signal in searches for primordial gravitational waves.
We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by calculating the levels of potential contaminants and performing a number of null tests. The resulting convergence power spectrum at 2-degree angular scales measures the amplitude of matter density fluctuations on comoving length scales of around 100 Mpc at redshifts around 0.5 to 3. The measured amplitude of the signal agrees with Lambda Cold Dark Matter cosmology predictions. Since the amplitude of the convergence power spectrum scales as the square of the amplitude of the density fluctuations, the 4-sigma detection of the lensing signal measures the amplitude of density fluctuations to 12%.
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