Integrated Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) in the recent CMB data

We have made a Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) using the WMAP bispectrum and power spectrum. In our analysis, we have simultaneously constrained f_NL and cosmological parameters so that the uncertainties of cosmological parameters can properly propagate to the f_NL estimation. Investigating the parameter likelihoods deduced from MCMC samples, we find slight deviation from Gaussian shape, which makes a Fisher matrix estimation less accurate. Therefore, we have estimated the confidence interval of f_NL by exploring the parameter likelihood without using the Fisher matrix. We find that the best-fit values of our analysis make a good agreement with other results, but the confidence interval is slightly different.Comment: v3: mean likelihoods added, v4: 2D likelihood added, typos corrected, v5: the point sharpene

How to make a clean separation between CMB E and B modes with proper foreground masking

We investigate the E/B decomposition of CMB polarization on a masked sky. In real space, operators of E and B mode decomposition involve only differentials of CMB polarization. We may, therefore in principle, perform a clean E/B decomposition from incomplete sky data. Since it is impractical to apply second derivatives to observation data, we usually rely on spherical harmonic transformation and inverse transformation, instead of using real-space operators. In spherical harmonic representation, jump discontinuities in a cut sky produces Gibbs phenomenon, unless a spherical harmonic expansion is made up to an infinitely high multipole. By smoothing a foreground mask, we may suppress the Gibbs phenomenon effectively in a similar manner to apodization of a foreground mask discussed in other works. However, we incur foreground contamination by smoothing a foreground mask, because zero-value pixels in the original mask may be rendered non-zero by the smoothing process. In this work, we investigate an optimal foreground mask, which ensures proper foreground masking and suppresses Gibbs phenomenon. We apply our method to a simulated map of the pixel resolution comparable to the Planck satellite. The simulation shows that the leakage power is lower than unlensed CMB B mode power spectrum of tensor-to-scalar ratio $r\sim 1\times10^{-7}$. We compare the result with that of the original mask. We find that the leakage power is reduced by a factor of $10^{6} \sim 10^{9}$ at the cost of a sky fraction $0.07$, and that the enhancement is highest at lowest multipoles. We confirm that all the zero-value pixels in the original mask remain zero in our mask. The application of this method to the Planck data will improve the detectability of primordial tensor perturbation.Comment: v2: typos corrected, v3: matched with the published version (the clarity improved) v4: a typo corrected v5: a bibliography file error fixe

Optimizing interferometer experiments for CMB B mode measurement

The sensitivity of interferometers with linear polarizers to the CMB E and B mode are variant under the rotation of the polarizer frame, while interferometer with circular polarizers are equally sensitive to E and B mode. We present analytically and numerically that the diagonal elements of window functions for CMB E/B power spectra are maximized in interferometric measurement of linear polarization, when the polarizer frame is in certain rotation from the associated baseline. We also present the simulated observation to show that the 1-$\sigma$ errors on E/B mode power spectrum estimation are variant under the polarizer frame rotation in the case of linear polarizers, while they are invariant in the case of circular polarizers. Simulation of the configuration similar to the DASI shows that minimum 1-$\sigma$ error on B mode in interferometer measurement with linear polarizers is 26% of that in interferometric measurement with circular polarizers. The simulation also shows that the E/B mixing in interferometer measurement with linear polarizers can be as low as 23% of that in interferometric measurement with circular polarizers. It is not always possible to physically align the polarizer frame with all the associated baselines in the case of an interferometer array (N$>$2). There exist certain linear combinations of visibilities, which are equivalent to visibilities of the optimal polarizer frame rotation. We present the linear combinations, which enables B mode optimization for an interferometer array (N$>$2).Comment: v2: file error corrected, v3: a footnote added, v4: a typo corrected v10: some pdf file problem fixe

Lack of angular correlation and odd-parity preference in CMB data

We have investigated the angular correlation in the recent CMB data. In addition to the known large-angle correlation anomaly, we find the lack of correlation at small angles with high statistical significance. We have investigated various non-cosmological contamination and additionally WMAP team's simulated data. However, we have not found a definite cause. In the angular power spectrum of WMAP data, there exist anomalous odd-parity preference at low multipoles. Noting the equivalence between the power spectrum and the correlation, we have investigated the association between the lack of large-angle correlation and the odd-parity preference. From our investigation, we find that the odd-parity preference at low multipoles is, in fact, a phenomenological origin of the lack of large-angle correlation. Futher investigation is required to find out whether the origin of the anomaly is cosmological or due to unaccounted systematics. The data from Planck surveyor, which has systematics distinct from the WMAP, will greatly help us to resolve its origin.Comment: v3: typos corrected, v4: plots updated, v5: analysis extended, v6: matched with the accepted version in ApJ (minor change

CMB data constraint on self-annihilation of dark matter particles

Recently, self-annihilation of dark matter particles is proposed to explain the "WMAP Haze" and excess of energetic positrons and electrons in ATIC and PAMELA results. If self-annihilation of dark matter occurs around the recombination of cosmic plasma, energy release from self-annihilation of dark matter delays the recombination, and hence affects CMB anisotropy. By using the recent CMB data, we have investigated the self-annihilation of dark matter particles. In this investigation, we do not find statistically significant evidence, and impose an upper bound on / m_chi. The upcoming data from Planck surveyor and the Fermi Gamma-ray telescope will allow us to break some of parameter degeneracy and improve constraints on self-annihilation of dark matter particles.Comment: a talk presented at the Invisible Universe International Conference at the Palais de l'UNESCO, Paris, v2: references adde

Parametric tension between even and odd multipole data of WMAP power spectrum: unaccounted contamination or missing parameters?

There exist power contrast in even and odd multipoles of WMAP power spectrum at low and intermediate multipole range. This anomaly is explicitly associated with the angular power spectrum, which are heavily used for cosmological model fitting. Having noted this, we have investigated whether even(odd) multipole data set is consistent with the WMAP concordance model. Our investigation shows WMAP concordance model does not make a good fit for even(odd) multipole data set, and there exist tension between two data subsets. Noting tension is highest in primordial power spectrum parameters, we have additionally considered a running spectral index, but find tension increases to even a higher level. We believe these parametric tensions may be indications of unaccounted contamination or imperfection of the model.Comment: v2: Latex error fixed, v3: matched with the accepted version in ApJL, conclusion unchange

Limits on anisotropic inflation from the Planck data

Temperature anisotropy of the cosmic microwave background offers a test of the fundamental symmetry of spacetime during cosmic inflation. Violation of rotational symmetry yields a distinct signature in the power spectrum of primordial fluctuations as $P({\mathbf k})=P_0(k)[1+g_*(\hat{\mathbf k}\cdot\hat{\mathbf E}_{\rm cl})^2]$, where $\hat{\mathbf E}_{\rm cl}$ is a preferred direction in space and $g_*$ is an amplitude. Using the \textit{Planck} 2013 temperature maps, we find no evidence for violation of rotational symmetry, $g_*=0.002\pm 0.016$ (68% CL), once the known effects of asymmetry of the \textit{Planck} beams and Galactic foreground emission are removed.Comment: 5 pages, 2 figures. (v2) References added. A typo fixed. (v3) Various confidence levels included, Journal reference added (v4) error of a duplicated pdf file fixe

Cosmological Alfv\'en waves in the recent CMB data, and the observational bound on the primordial vector perturbation

In the presence of the primordial magnetic field, initial vector (vorticity) perturbations produce cosmological Alfven waves and leave imprints on cosmic microwave background (CMB) temperature and polarization anisotropy. We have investigated imprints of cosmological Alfven waves in CMB anisotropy. For data constraints, we have used the power spectrum of the recent CMB observations, and correlations estimated from WMAP Internal Linear Combination (ILC) maps. Our analysis shows 3 sigma evidence of cosmological Alfven waves. Using the 3 sigma limit from our analysis and the Alfven velocity limit from the total energy density constraint, we impose a lower bound on the amplitude of primordial vector perturbation: 4*10^-12 at k_0=0.002/Mpc.Comment: v2: change in analysis method and confidence interval improved v3: typos corrected v4: a typo in Eq. 36 corrected v5: lower bound on vector perturbation in more compliant form for ease of comparison, references adde

Direct reconstruction of spherical harmonics from interferometer observations of the CMB polarization

Interferometric observation of the CMB polarization can be expressed as a linear sum of spherical harmonic coefficients $a_{\pm 2,lm}$ of the CMB polarization. The linear weight for $a_{\pm 2,lm}$ depends on the observational configuration such as antenna pointing, baseline orientation, and spherical harmonic number $l,m$. Since an interferometer is sensitive over a finite range of multipoles, $a_{\pm 2,lm}$ in the range can be determined by fitting $a_{\pm 2,lm}$ for visibilities of various observational configurations. The formalism presented in this paper enables the determination of $a_{\pm 2,lm}$ directly from spherical harmonic spaces without spherical harmonic transformation of pixellized maps. The result of its application to a simulated observation is presented with the formalism.Comment: v2: references updated, v3: a typo corrected v9: a pdf file problem fixe

Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation

The Integrated Sachs-Wolfe (ISW) effect produces a secondary temperature anisotropy of CMB. The main contribution comes from z<2, where dark energy leads to a decay of potentials. As the same photons are gravitationally lensed by these decaying potentials, there exists a high degree of correlation between the ISW effect and CMB lensing, leading to a non-zero three-point correlation (bispectrum) of the observed temperature anisotropy. This ISW-lensing bispectrum, whose shape resembles that of the so-called "local-form" primordial bispectrum parametrized by fNL, is known to be the largest contamination of fNL. In order to avoid a spurious detection of primordial non-Gaussianity, we need to remove the ISW-lensing bias. In this work, we investigate three debiasing methods: (I) subtraction of an expected, ensemble average of the ISW-lensing bispectrum; (II) subtraction of a measured ISW-lensing bispectrum; and (III) direct subtraction of an estimated ISW signal from an observed temperature map. One may use an estimation of the ISW map from external non-CMB data or that from the CMB data themselves. As the methods II and III are based on fewer assumptions about the nature of dark energy, they are preferred over the method I. While the methods I and II yield unbiased estimates of fNL with comparable error bars, the method III yields a biased result when the underlying primordial fNL is non-zero and the ISW map is estimated from a lensing potential reconstructed from the observed temperature map. One of the sources of the bias is a lensing reconstruction noise bias which is independent of fNL and can be calculated precisely, but other fNL-dependent terms are difficult to compute reliably. We thus conclude that the method II is the best, model-independent way to remove the ISW-lensing bias of fNL, enabling us to test the physics of inflation with smaller systematic errors.Comment: 17 pages, comments are welcomed v2: references added, v3: references adde