Cosmic Background Explorer Differential Microwave Research Articles

Astrophysical component separation of COBE-DMR 4-yr data with FastICA

We present an application of the Fast Independent Component Analysis (FastICA) method to the Cosmic Background Explorer Differential Microwave Radiometer (COBE-DMR) 4-yr data. Although the signal-to-noise (S/N) ratio in the COBE-DMR data is typically ∼1, the approach is able to extract the cosmic microwave background (CMB) signal with high confidence from high galactic latitude regions. However, the foreground emission components have too low a S/N ratio to be reconstructed by this method (moreover, the number of components which can be reconstructed is directly limited by the number of input channels). The reconstructed CMB map shows the expected frequency scaling of the CMB and, fitting for the rms quadrupole normalization Qrms-PS and primordial spectral index n we find results in excellent agreement with those derived from the minimum-noise combination of the 90- and 53-GHz DMR channels without galactic emission correction. We extend the analysis by including additional channels (priors): the Haslam map of radio emission at 408 MHz and the Diffuse Infrared Background Experiment (DIRBE) 140-μm map of galactic infrared emission. The FastICA algorithm is now able to both detect galactic foreground emission and separate it from the dominant CMB signal. Fitting again for Qrms-PS and n we find good agreement with the results of Górski et al. where galactic emission has been taken into account by means of correlation analysis of the DMR signal. We investigate the ability of FastICA to evaluate the extent of foreground contamination in the COBE-DMR data further including an all-sky Hα survey to determine a reliable free-free. The derived frequency scalings of the recovered foregrounds are consistent with previous correlation studies. After subtraction of the thermal dust emission as in model 7 of Finkbeiner, Davis & Schlegel, we find a clear indication of an anomalous dust-correlated component which is the dominant foreground emission at 31.5 GHz and which is well fitted by a power-law spectral shape ν−β with β∼ 2.5 in agreement with Banday et al.

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

We perform a discrete wavelet analysis of the Cosmic Background Explorer differential microwave radiometer (DMR) 4-yr sky maps and find a significant scale-scale correlation on angular scales from about 11\ifmmode^\circ\else\textdegree\fi{} to 22\ifmmode^\circ\else\textdegree\fi{}, only in the DMR face centered on the north galactic pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22\ifmmode^\circ\else\textdegree\fi{}, or the standard inflation plus cold dark matter paradigm is ruled out at the $>99%$ confidence level.

Estimating the power spectrum of the cosmic microwave background

We develop two methods for estimating the power spectrum, ${C}_{\mathcal{l}},$ of the cosmic microwave background from data and apply them to the Cosmic Background Explorer Differential Microwave Radiometer 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 ${C}_{\mathcal{l}}$s. The quadratic estimator can also be used to determine directly 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.

Limits to global rotation and shear from the COBE DMR four-year sky maps

Small departures from a homogeneous isotropic spacetime create observable features in the large-scale anisotropy of the cosmic microwave background. We cross correlate the maps of the cosmic microwave background anisotropy from the Cosmic Background Explorer Differential Microwave Radiometers four-year data set with template maps from Bianchi type VII${}_{h}$ cosmological models to limit global rotation or shear in the early universe. On the largest scales, spacetime is well described by the Friedmann-Robertson-Walker metric, with departures from isotropy about each spatial point limited to shear $\ensuremath{\sigma}{/H}_{0}<{10}^{\ensuremath{-}9}$ and rotation $\ensuremath{\omega}{/H}_{0}<6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ for $0.1<~{\ensuremath{\Omega}}_{0}<~1$.

Signal-to-noise eigenmode analysis of the two-year COBE maps.

To test best a theory of cosmic microwave background fluctuations, anisotropy maps [here the two-year Cosmic Background Explorer differential microwave radiometer (DMR) $53,90,31\mathrm{GHz}$ $a$ and $b$ and the Far-Infrared Survey (FIRS) 170 GHz maps] are expanded in a complete basis of linear combinations of pixel amplitudes---statistically independent for both the noise and the signal. Bayesian analysis of a 2-parameter inflation-inspired theory shows the overall band-power and spectral tilt index ${\ensuremath{\nu}}_{\ensuremath{\Delta}T}+1$ for all maps agree within $1\ensuremath{\sigma}$, ${(1.1\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{}}^{2}$ and $1.27\ifmmode\pm\else\textpm\fi{}0.33$ (compatible with inflation values, $\ensuremath{\sim}0.8\ensuremath{-}1.2$); and $S/N$ filtering of the DMR maps reveals the same large-scale structural features.

An infrared cutoff revealed by the two years of COBE observations of cosmic temperature fluctuations.

We show that a good fitting to the first two years of observations by the Cosmic Background Explorer Differential Microwave Radiometers of the two-point angular correlation function of cosmic background radiation (CBR) temperature is given by models with a nonzero infrared cutoff ${k}_{min}$ in the spectrum of the primordial density perturbations. If this cutoff comes from the finiteness of the universe, say, a topological T3 model, we find ${k}_{min}\ensuremath{\sim}(0.3\ensuremath{-}1.1)\ensuremath{\pi}\frac{{\mathrm{H}}_{0}}{c}$ with confidence level 95%. Such a nonzero ${k}_{min}$ universe would also give a better match to the observations both of the rms quadrupole anisotropy of CBR and of galaxy clustering.

Tensor perturbations in inflationary models as a probe of cosmology.

In principle, the tensor metric (gravity-wave) perturbations that arise in inflationary models can, beyond probing the underlying inflationary model, provide information about the Universe: ionization history, presence of a cosmological constant, and epoch of matter-radiation equality. Because tensor perturbations give rise to the anisotropy of the cosmic background radiation (CBR) solely through the Sachs-Wolfe effect we are able to calculate analytically their contribution to the variance of the multipole moments of the CBR temperature anisotropy. In so doing, we carefully take account of the effect of tensor perturbations that entered the Hubble radius during both the matter-dominated and radiation-dominated epochs by means of a transfer function. (Previously, only those modes that entered during the matter era were properly taken into account.) The striking feature in the spectrum of multipole amplitudes is a dramatic falloff for l\ensuremath{\gtrsim} \ensuremath{\surd}1+${\mathit{z}}_{\mathrm{LSS}}$ , where ${\mathit{z}}_{\mathrm{LSS}}$ is the redshift of the last-scattering surface, which depends upon the ionization history of the Universe. Finally, using our transfer function we provide a more precise formula for the energy density in stochastic gravitational waves from inflation, and, using the Cosmic Background Explorer Differential Microwave Radiometer (COBE DMR) quadrupole normalization, we express this energy density in terms of the ``tilt'' of the spectrum of tensor perturbations alone and show that it is unlikely that the stochastic background of gravity waves can be detected directly in the foreseeable future.