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Register a new userA Fast Gridded Method for the Estimation of the Power Spectrum of the CMB from Interferometer Data with Application to the Cosmic Background Imager
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We describe an algorithm for the extraction of the angular power spectrum of an intensity field, such as the cosmic microwave background (CMB), from interferometer data. This new method, based on the gridding of interferometer visibilities in the aperture plane followed by a maximum likelihood solution for bandpowers, is much faster than direct likelihood analysis of the visibilities, and deals with foreground radio sources, multiple pointings, and differencing. The gridded aperture-plane estimators are also used to construct Wiener-filtered images using the signal and noise covariance matrices used in the likelihood analysis. Results are shown for simulated data. The method has been used to determine the power spectrum of the cosmic microwave background from observations with the Cosmic Background Imager, and the results are given in companion papers.
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We review the recently published results from the CBIs first season of observations. Angular power spectra of the CMB were obtained from deep integrations of 3 single fields covering a total of 3 deg^2 and 3 shallower surveys of overlapping (mosaiced) fields covering a total of 40 deg^2. The observations show a damping of the anisotropies at high-l as expected from the standard scenarios of recombination. We present parameter estimates obtained from the data and discuss the significance of an excess at l>2000 observed in the deep fields.
We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from earlier ones in that the power spectrum is estimated directly from time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been masked out to remove foreground contamination, leaving a pure CMB signal, but incomplete sky coverage. The first method (DQML) is derived as the optimal quadratic estimator, which simultaneously yields an unbiased spectrum estimate and minimizes its variance. We successfully apply it to multipoles up to $ell$=200. The second method is derived as a weak-signal approximation from the first one. It yields an unbiased estimate for the full multipole range, but relaxes the requirement of minimal variance. We validate the methods with simulations for the 70 GHz channel of {tt Planck} surveyor, and demonstrate that we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$ spectra up to multipole $ell$=1500. Together the two methods cover the complete multipole range with no gap in between.
A new field theory formulation is presented for the analysis of the CMB power spectrum distribution in the cosmology. The background-field formalism is fully used. Stimulated by the recent idea of the {it emergent} gravity, the gravitational (metric) field $g_mn$ is not taken as the quantum-field, but as the background field. The statistical fluctuation effect of the metric field is taken into account by the path (hyper-surface)-integral over the space-time. Using a simple scalar model on the curved (dS$_4$) space-time, we explain the above things with the following additional points: 1) Clear separate treatment of the classical effect, the statistical effect and the quantum effect; 2) The cosmological fluctuation comes not from the quantum gravity but from the unkown microscopic movement; 3) IR parameter ($ell$) is introduced for the time axis as the periodicity. Time reversal(Z$_2$)-symmetry is introduced in order to treat the problem separately with respect to the Z$_2$ parity. This procedure much helps both UV and IR regularization to work well.
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.
We discuss the nature of the possible high-l excess in the Cosmic Microwave Background (CMB) anisotropy power spectrum observed by the Cosmic Background Imager (CBI). We probe the angular structure of the excess in the CBI deep fields and investigate whether it could be due to the scattering of CMB photons by hot electrons within clusters, the Sunyaev-Zeldovich (SZ) effect. We estimate the density fluctuation parameters for amplitude, sigma_8, and shape, Gamma, from CMB primary anisotropy data and other cosmological data. We use the results of two separate hydrodynamical codes for Lambda-CDM cosmologies, consistent with the allowed sigma_8 and Gamma values, to quantify the expected contribution from the SZ effect to the bandpowers of the CBI experiment and pass simulated SZ effect maps through our CBI analysis pipeline. The result is very sensitive to the value of sigma_8, and is roughly consistent with the observed power if sigma_8 ~ 1. We conclude that the CBI anomaly could be a result of the SZ effect for the class of Lambda-CDM concordance models if sigma_8 is in the upper range of values allowed by current CMB and Large Scale Structure (LSS) data.
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