Primordial Non-Gaussianity in the Cosmic Microwave Background

In the last few decades, advances in observational cosmology have given us a standard model of cosmology. We know the content of the universe to within a few percent. With more ambitious experiments on the way, we hope to move beyond the knowledge of what the universe is made of, to why the universe is the way it is. In this review paper we focus on primordial non-Gaussianity as a probe of the physics of the dynamics of the universe at the very earliest moments. We discuss 1) theoretical predictions from inflationary models and their observational consequences in the cosmic microwave background (CMB) anisotropies; 2) CMB--based estimators for constraining primordial non-Gaussianity with an emphasis on bispectrum templates; 3) current constraints on non-Gaussianity and what we can hope to achieve in the near future; and 4) non-primordial sources of non-Gaussianities in the CMB such as bispectrum due to second order effects, three way cross-correlation between primary-lensing-secondary CMB, and possible instrumental effects.Comment: 27 pages, 8 figures; Invited Review for the Journal "Advances in Astronomy"; references adde

Probing Primordial Magnetism with Off-Diagonal Correlators of CMB Polarization

Primordial magnetic fields (PMF) can create polarization $B$-modes in the cosmic microwave background (CMB) through Faraday rotation (FR), leading to non-trivial 2-point and 4-point correlators of the CMB temperature and polarization. We discuss the detectability of primordial magnetic fields using different correlators and evaluate their relative merits. We have fully accounted for the contamination by weak lensing, which contributes to the variance, but whose contribution to the 4-point correlations is orthogonal to that of FR. We show that a Planck-like experiment can detect scale-invariant PMF of nG strength using the FR diagnostic at 90GHz, while realistic future experiments at the same frequency can detect 10^{-10} G. Utilizing multiple frequencies will improve on these prospects, making FR of CMB a powerful probe of scale-invariant PMF.Comment: 11 pages, 4 figures; unit typos fixed in fig 1 and

Primordial B-mode Diagnostics and Self Calibrating the CMB Polarization

Distortions in the primordial cosmic microwave background (CMB) along the line-of-sight can be modeled and described using 11 fields. These distortion fields correspond to various cosmological signals such as weak gravitational lensing of the CMB by large-scale structure, screening from patchy reionization, rotation of the plane of polarization due to magnetic fields or parity violating physics. Various instrumental systematics such as gain fluctuations, pixel rotation, differential gain, pointing, differential ellipticity are also described by the same distortion model. All these distortions produce B-mode that contaminate the primordial tensor B-modes signal. In this paper we show that apart from generating B-modes, each distortion uniquely couples different modes (\bfl_1\ne \bfl_2) of the CMB anisotropies, generating $$ correlations which for the primordial CMB are zero. We describe and implement unbiased minimum variance quadratic estimators which using the off diagonal correlations in the CMB can extract the map of distortions. We perform Monte-Carlo simulations to characterize the estimators and illustrate the level of distortions that can be detected with current and future experiments. The estimators can be used to look for cosmological signals, or to check for any residual systematics in the data. As a specific example of primordial tensor B-mode diagnostics we compare the level of minimum detectable distortions using our method with maximum allowed distortion level for the B-modes detection. We show that for any experiment, the distortions will be detected at high significance using correlations before they would show up as spurious B-modes in the power spectrum.Comment: 14 pages, 4 figure

Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization

Following Kamionkowski (2008), a quadratic estimator of the rotation of the plane of polarization of the CMB is constructed. This statistic can estimate a spatially varying rotation angle. We use this estimator to quantify the prospects of detecting such a rotation field with forthcoming experiments. For PLANCK and CMBPol we find that the estimator containing the product of the E and B components of the polarization field is the most sensitive. The variance of this EB estimator, N(L) is roughly independent of the multipole L, and is only weakly dependent on the instrumental beam. For FWHM of the beam size ~ 5'-50', and instrument noise $\Delta_p ~ 5-50 uK-arcmin, the scaling of variance N(L) can be fitted by a power law N(L)=3.3 x 10^{-7} \Delta^2_p (FWHM)^{1.3} sq-deg. For small instrumental noise \Delta_p \leq 5 uK-arcmin, the lensing B-modes become important, saturating the variance to ~10^{-6} sq-deg even for an ideal experiment. Upcoming experiments like PLANCK will be able to detect a power spectrum of the rotation angle, C^{\alpha \alpha}(L), as small as 0.01 sq-deg, while futuristic experiment like CMBPol will be able to detect rotation angle power spectrum as small as 2.5 x 10^{-5} sq-deg. We discuss the implications of such constraints, both for the various physical effects that can rotate the polarization as photons travel from the last scattering surface as well as for constraints on instrumental systematics that can also lead to a spurious rotation signal. Rotation of the CMB polarization generates B-modes which will act as contamination for the primordial B-modes detection. We discuss an application of our estimator to de-rotate the CMB to increase the sensitivity for the primordial B-modes.Comment: 11 pages, 5 figure

Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams

We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O(\phi^4) in the lensing potential $\phi$. We consider both the diagonal noise TTTT, EBEB, etc. and, for the first time, the off-diagonal noise TTTE, TBEB, etc. The previously noted large O(\phi^4) term in the second order noise is identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the $\phi$ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one $B$ component of the CMB, such as EEEB.Comment: 17 pages, 17 figure

Gravitational Lensing of the CMB: a Feynman Diagram Approach

We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to ${\mathcal O}(\phi^4)$ in the lensing potential $\phi$. The previously noted large ${\mathcal O}(\phi^4)$ term can be significantly reduced by a reorganization of the $\phi$ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields.Comment: 5 pages, 8 figures, v2: journal versio