Statistical Isotropy of CMB Polarization Maps

We formulate statistical isotropy of CMB anisotropy maps in its most general form. We also present a fast and orientation independent statistical method to determine deviations from statistical isotropy in CMB polarization maps. Importance of having statistical tests of departures from SI for CMB polarization maps lies not only in interesting theoretical motivations but also in testing cleaned CMB polarization maps for observational artifacts such as residuals from polarized foreground emission. We propose a generalization of the Bipolar Power Spectrum (BiPS) to polarization maps. Application to the observed CMB polarization maps will be soon possible after the release of WMAP three year data. As a demonstration we show that for E-polarization this test can detect breakdown of statistical isotropy due to polarized synchrotron foreground.Comment: 6 pages, 2 figures, Conclusions & results unchanged; Extension to cutsky included (discussion & references added); Matches version accepted to Phys. Rev. D Rapid Com

Odd-Parity Bipolar Spherical Harmonics

Bipolar spherical harmonics (BiPoSHs) provide a general formalism for quantifying departures in the cosmic microwave background (CMB) from statistical isotropy (SI) and from Gaussianity. However, prior work has focused only on BiPoSHs with even parity. Here we show that there is another set of BiPoSHs with odd parity, and we explore their cosmological applications. We describe systematic artifacts in a CMB map that could be sought by measurement of these odd-parity BiPoSH modes. These BiPoSH modes may also be produced cosmologically through lensing by gravitational waves (GWs), among other sources. We derive expressions for the BiPoSH modes induced by the weak lensing of both scalar and tensor perturbations. We then investigate the possibility of detecting parity-breaking physics, such as chiral GWs, by cross-correlating opposite parity BiPoSH modes with multipole moments of the CMB polarization. We find that the expected signal-to-noise of such a detection is modest.Comment: 19 pages, 4 figures, Accepted to PR

Spectroscopy of Cosmic topology

Einstein's theory of gravitation that governs the geometry of space-time, coupled with spectacular advance in cosmological observations, promises to deliver a `standard model' of cosmology in the near future. However, local geometry of space constrains, but does not dictate the topology of the cosmos. hence, Cosmic topology has remained an enigmatic aspect of the `standard model' of cosmology. Recent advance in the quantity and quality of observations has brought this issue within the realm of observational query. The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic consequence of non trivial cosmic topology arising from to the imposed `crystallographic' periodicity on the eigenstates of the Laplacian. The sky maps of Cosmic Microwave Background (CMB) anisotropy and polarization most promising observations that would carry signatures of a violation of statistical isotropy and homogeneity. Hence, a measurable spectroscopy of cosmic topology is made possible using the Bipolar power spectrum (BiPS) of the temperature and polarization that quantifies violation of statistical isotropy

Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis

The statistical expectation values of the temperature fluctuations of the Cosmic Microwave Background (CMB) are assumed to be preserved under rotations of the sky. We investigate the Statistical Isotropy (SI) of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using Bipolar Power Spectrum (BiPS) proposed in [Hajian & Souradeep 2003]. The method can probe specific regions in multipole space using appropriate window functions. The BiPS is estimated for full sky CMB anisotropy maps based on the first year WMAP data using a range of window functions. The BiPS spectra computed for both full sky maps for all our window functions are consistent with zero, roughly within $2 \sigma$. The null BiPS results may be interpreted as an absence of strong violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to $l\sim60$. However, pending a careful direct comparison, our results do not necessarily conflict with the specific SI related anomalies reported using other statistical tests.Comment: 5 pages, 4 figures, trimmed in size, results and conclusions unchanged, matches version to appear in ApJ. Let

Testing Global Isotropy of Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Data: Temperature Analysis

We examine statistical isotropy of large scale anisotropies of the Internal Linear Combination (ILC) map, based on three year WMAP data. Our study reveals no significant deviation from statistical isotropy on large angular scales of 3-year ILC map. Comparing statistical isotropy of 3-year ILC map and 1-year ILC map, we find a significant improvement in 3-year ILC map which can be due to the gain model, improved ILC map processing and foreground minimization

Dipole leakage and low CMB multipoles

A number of studies of WMAP-7 have highlighted that the power at the low multipoles in CMB power spectrum is lower than their theoretically predicted value. Angular correlation between the orientations of these low multipoles have also been discovered. While these observations may have cosmological ramification, it is important to investigate possible observational artifacts that can mimic them. The CMB dipole, which is much higher than the quadrupole, can get leaked to the higher multipoles due to the non-circular beam of the CMB experiment. In this paper, an analytical method has been developed and simulations are carried out to study the effect of the non-circular beam on power leakage from the dipole. It has been shown that the small, but non-negligible power from the dipole can get transferred to the quadrupole and the higher multipoles due to the non-circular beam. Simulations have also been carried out for Planck scan strategy, and comparative results between WMAP and Planck have been presented

Statistical Isotropy violation of the CMB brightness fluctuations

Certain anomalies at large angular scales in the cosmic microwave background measured by WMAP have been suggested as possible evidence of breakdown of statistical isotropy(SI). Most CMB photons free-stream to the present from the surface of last scattering. It is thus reasonable to expect statistical isotropy violation in the CMB photon distribution observed now to have originated from SI violation in the baryon-photon fluid at last scattering, in addition to anisotropy of the primordial power spectrum studied earlier in literature. We consider the generalized anisotropic brightness distribution fluctuations, $\Delta(\vec{k}, \hat{n}, \tau)$ (at conformal time $\tau$) in contrast to the SI case where it is simply a function of $|\vec{k}|$ and $\hat{k} \cdot \hat{n}$. The brightness fluctuations expanded in Bipolar Spherical Harmonic (BipoSH) series, can then be written as $\Delta_{\ell_1 \ell_2}^{L M}(\vec{k}, \tau)$ where $L > 0$ terms encode deviations from statistical isotropy. We study the evolution of $\Delta_{\ell_1 \ell_2}^{L M}(\vec{k}, \tau)$ from non-zero terms $\Delta_{\ell_3 \ell_4}^{L M}(\vec{k}, \tau_s)$ at last scattering. Similar to the SI case, power at small spherical harmonic (SH) multipoles of $\Delta_{\ell_3 \ell_4}^{L M}(\vec{k},\tau_s)$ at the last scattering, is transferred to $\Delta_{\ell_1 \ell_2}^{L M}(\vec{k}, \tau)$ at larger SH multipoles. The structural similarity is more apparent in the asymptotic expression for large values of the final SH multipoles. This formalism allows an elegant identification of any SI violation observed today to a possible origin in the SI violation present in the baryon-photon fluid (eg., due to the presence of significant magnetic field).Comment: 14 pages, 4 figures, added illustrative example of SI violation in baryon-photon fluid, matches version accepted for publication in Phys. Rev.

Galactic Foreground Constraints from the Python V Cosmic Microwave Background Anisotropy Data

We constrain Galactic foreground contamination of the Python V cosmic microwave background anisotropy data by cross correlating it with foreground contaminant emission templates. To model foreground emission we use 100 and 12 $\mu$m dust emission templates and two point source templates based on the PMN survey. The analysis takes account of inter-modulation correlations in 8 modulations of the data that are sensitive to a large range of angular scales and also densely sample a large area of sky. As a consequence the analysis here is highly constraining. We find little evidence for foreground contamination in an analysis of the whole data set. However, there is indication that foregrounds are present in the data from the larger-angular-scale modulations of those Python V fields that overlap the region scanned earlier by the UCSB South Pole 1994 experiment. This is an independent consistency cross-check of findings from the South Pole 1994 data.Comment: 15 pages, 1 figure, ApJ accepted versio

Estimation of Primordial Spectrum with post-WMAP 3 year data

In this paper we implement an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the WMAP 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat LCDM cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a `best fit' power law spectrum up to \Delta \chi^2_{eff} \approx -30. We use Discrete Wavelet Transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, for a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat CDM model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.Comment: 13 pages, 4 figures, uses Revtex4, new analysis and results, references added, matches version accepted to Phys. Rev.