Cosmic Microwave Background Polarization Fields Research Articles

Back to the features: assessing the discriminating power of future CMB missions on inflationary models

Future Cosmic Microwave Background (CMB) experiments will deliver extremely accurate measurements of the E-modes pattern of the CMB polarization field. Given the sharpness of the E-modes transfer functions, such surveys make for a powerful detector of high-frequency signals from primordial features that may be lurking in current data sets. With a handful of toy models that increase the fit to the latest Planck data, but are of marginal statistical significance, we use a state-of-the-art forecast pipeline to illustrate the promising prospects to test primordial features in the next decade. Not only will future experiments allow us to detect such features in data, but they will also be able to discriminate between models and narrow down the physical mechanism originating them with high statistical significance. On the other hand, if the anomalies in the currently measured CMB spectra are just statistical fluctuations, all the current feature best fit candidates will be ruled out. Either way, our results show that primordial features are a clear target of forthcoming CMB surveys beyond the detection of tensor modes.

Statistical isotropy violation of CMB Polarization sky due to Lorentz boost

In the frame of a moving observer, the Cosmic Microwave Background (CMB) fluctuation exhibits violation of Statistical Isotropy (SI). The SI violation effect from our local motion on CMB temperature fluctuation has been measured in the recent Planck results. We calculate the effect of our local motion with velocity $(\beta \equiv |\boldsymbol v|/c= 1.23 \times 10^{-3})$ on CMB polarization field. The Lorentz transformation of the polarization field leads to aberration in the direction of incoming photons and also modulation of the Stokes parameters, which results in mixing of power between different CMB multipoles. We show that for small values of $\beta$, the effect on the angular power spectra that corresponds to the diagonal terms in the spherical harmonic space is at $O(\beta^2)$. But non-zero off-diagonal terms at the linear order in $\beta$ could provide a measurable signature of SI violation in the Bipolar Spherical Harmonic (BipoSH) representation. We also calculate the measurability of $\beta$ from polarization maps from experiments like Planck and PRISM. It is possible to measure $\beta$ from the ideal, cosmic variance limited BipoSH spectra of $EE$, $TE$, $BB$, but not in $EB$ and $TB$. With the instrumental noise of and angular resolution of Planck, it is not possible to measure $\beta$ with high statistical significance from BipoSH spectra of polarization. PRISM can measure $\beta$ with high significance in both $EE$ and $TE$ BipoSH spectra, but not in $BB$, $EB$ and $TB$ BipoSH spectra.

A new third-order cosmic shear statistic: separating E-/B-mode correlations on a finite interval

Decomposing the shear signal into E and B modes properly, i.e. without leakage of B modes into the E-mode signal and vice versa, has been a long-standing problem in weak gravitational lensing. At the two-point level this problem was resolved by developing the so-called ring statistic, and later the COSEBIs; however, extending these concepts to the three-point level is far from trivial. Currently used methods to decompose shear three-point correlation functions (3PCFs) into E and B modes require knowledge of the 3PCF down to arbitrary small scales. This implies that the 3PCF needs to be modelled on scales smaller than the minimum separation of two galaxies and will subsequently be biased towards the model, or, in the absence of a model, the statistic is affected by E-/B-mode leakage (or mixing). In this paper, we derive a new third-order E-/B-mode statistic that performs the decomposition using the 3PCF only on a finite interval, and thereby is free of any E-/B-mode leakage while at the same time relying solely on information from the data. In addition, we relate this third-order ring statistic to the convergence field, thereby enabling a fast and convenient calculation of this statistic from numerical simulations. We note that our new statistic should be applicable to corresponding E-/B-mode separation problems in the cosmic microwave background polarization field.

Testable polarization predictions for models of CMB isotropy anomalies

Anomalies in the large-scale cosmic microwave background (CMB) temperature sky measured by the Wilkinson Microwave Anisotropy Probe have been suggested as possible evidence for a violation of statistical isotropy on large scales. In any physical model for broken isotropy, there are testable consequences for the CMB polarization field. We develop simulation tools for predicting the polarization field in models that break statistical isotropy locally through a modulation field. We study two different models: dipolar modulation, invoked to explain the asymmetry in power between northern and southern ecliptic hemispheres, and quadrupolar modulation, posited to explain the alignments between the quadrupole and octopole. For the dipolar case, we show that predictions for the correlation between the first 10 multipoles of the temperature and polarization fields can typically be tested at better than the 98% CL. For the quadrupolar case, we show that the polarization quadrupole and octopole should be moderately aligned. Such an alignment is a generic prediction of explanations which involve the temperature field at recombination and thus discriminate against explanations involving foregrounds or local secondary anisotropy. Predicted correlations between temperature and polarization multipoles out to $\ensuremath{\ell}=5$ provide tests at the $\ensuremath{\sim}99%$ CL or stronger for quadrupolar models that make the temperature alignment more than a few percent likely. As predictions of anomaly models, polarization statistics move beyond the a posteriori inferences that currently dominate the field.

Fast quadratic power spectrum estimators and the E– B decomposition

We describe a fast, quadratic power spectrum estimator for cosmic microwave background polarization fields, based on heuristically-weighted correlation functions. The method can handle real-world effects such as inhomogeneous or correlated noise, and arbitrary sky cuts. A significant feature is that the electric and magnetic polarization powers are separated exactly in the mean, even for observations covering only a small region of the sky, and with a negligible increase in computational cost. The method is illustrated with simulations for a large-area survey, and a future, deep magnetic-polarization survey.

HarmonicE/Bdecomposition for CMB polarization maps

The full sky cosmic microwave background polarization field can be decomposed into ``electric'' (E) and ``magnetic'' (B) components that are signatures of distinct physical processes. We give a general construction that achieves separation of E and B modes on arbitrary sections of the sky at the expense of increasing the noise. When E modes are present on all scales the separation of all of the B signal is no longer possible: there are inevitably ambiguous modes that cannot be separated. We discuss the practicality of performing $E/B$ decomposition on large scales with realistic nonsymmetric sky cuts, and show that separation on large scales is possible by retaining only the well supported modes. The large scale modes potentially contain a great deal of useful information, and $E/B$ separation at the level of the map is essential for clean detection of B without confusion from cosmic variance due to the E signal. We give simple matrix manipulations for creating pure E and B maps of the large scale signal for general sky cuts. We demonstrate that the method works well in a realistic case and give estimates of the performance with data from the Planck satellite. In the Appendix we discuss the simple analytic case of an azimuthally symmetric cut, and show that exact $E/B$ separation is possible on an azimuthally symmetric cut with a finite number of nonintersecting circular cuts around foreground sources.

Analyzing weak lensing of the cosmic microwave background using the likelihood function

Future experiments will produce high-resolution temperature maps of the cosmic microwave background (CMB) and are expected to reveal the signature of gravitational lensing by intervening large-scale structures. We construct all-sky maximum-likelihood estimators that use the lensing effect to estimate the projected density (convergence) of these structures, its power spectrum, and cross-correlation with other observables. This contrasts with earlier quadratic-estimator approaches that Taylor expanded the observed CMB temperature to linear order in the lensing deflection angle; these approaches gave estimators for the temperature-convergence correlation in terms of the CMB three-point correlation function and for the convergence power spectrum in terms of the CMB four-point correlation function, which can be biased and nonoptimal due to terms beyond the linear order. We show that for sufficiently weak lensing, the maximum-likelihood estimator reduces to the computationally less demanding quadratic estimator. The maximum likelihood and quadratic approaches are compared by evaluating the root-mean-square (rms) error and bias in the reconstructed convergence map in a numerical simulation; it is found that both the rms errors and bias are of order 1 percent for the case of Planck and of order 10–20 percent for a 1 arcminute beam experiment. We conclude that for recovering lensing information from temperature data acquired by these experiments, the quadratic estimator is close to optimal, but further work will be required to determine whether this is also the case for lensing of the CMB polarization field.

SIMULATION OF COSMIC MICROWAVE BACKGROUND POLARIZATION FIELDS FOR AMiBA EXPERIMENT

We have made a topological study of cosmic microwave background (CMB) polarization maps by simulating the AMiBA experiment results. A $\Lambda$CDM CMB sky is adopted to make mock interferometric observations designed for the AMiBA experiment. CMB polarization fields are reconstructed from the AMiBA mock visibility data using the maximum entropy method. We have also considered effects of Galactic foregrounds on the CMB polarization fields. The genus statistic is calculated from the simulated $Q$ and $U$ polarization maps, where $Q$ and $U$ are Stokes parameters. Our study shows that the Galactic foreground emission, even at low Galactic latitude, is expected to have small effects on the CMB polarization field. Increasing survey area and integration time is essential to detect non-Gaussian signals of cosmological origin through genus measurement.

Analysis of CMB polarization on an incomplete sky

The full sky cosmic microwave background polarization field can be decomposed into ``electric'' and ``magnetic'' components. Working in harmonic space we construct window functions that allow clean separation of the electric and magnetic modes from observations over only a portion of the sky. We explicitly demonstrate the method for azimuthally symmetric patches, but also present it in a form in principle applicable to arbitrarily shaped patches. From the window functions we obtain variables that allow for robust estimation of the magnetic component without risk of contamination from the probably much larger electric signal. The variables have a very simple noise properties, and further analysis using them should be no harder than analyzing the temperature field. For an azimuthally symmetric patch, such as that obtained from survey missions when the galactic region is removed, the exactly separated variables are fast to compute. We estimate the magnetic signal that could be detected by the Planck satellite in the absence of extra-galactic foregrounds. We also discuss the sensitivity of future experiments to tensor modes in the presence of a magnetic signal generated by weak lensing, and give lossless methods for analyzing the electric polarization field in the case that the magnetic component is negligible. A series of Appendixes review the spin weight formalism and give recursion relations for fast computation of the spin-weighted spherical harmonics and their inner products over azimuthally symmetric patches of the sphere. A further Appendix discusses the statistics of weak signal detection.

General Statistical Properties of the Cosmic Microwave Background Polarization Field

The distribution of the polarization of the cosmic microwave background (CMB) in the sky is determined by the hypothesis of random Gaussian distribution of the primordial density perturbations. This hypotheses is well motivated by the inflationary cosmology. Therefore, a test of the consistency of the statistical properties of the CMB polarization field with the Gaussianity of primordial density fluctuations is a realistic way to study the nature of primordial inhomogeneities in the universe. This paper contains theoretical predictions of the general statistical properties of the CMB polarization field. All results were obtained under the assumption of the Gaussian nature of the signal. We pay special attention to the following two problems: first, the classification and statistics of the singular points of the polarization field where polarization is equal to zero, and second, the topology of the contours of the value of the degree of polarization. We have investigated the percolation properties for the zones of strong and weak polarization. We have also calculated Minkowski functionals for the CMB polarization field. All results are analytical.