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We address the dual challenge of estimating deviations from Gaussianity arising in models of the early Universe, whilst retaining information necessary to assess whether a detection of non-Gaussianity is primordial. We do this by constructing a new statistic, the bispectrum-related power spectrum, which is constructed from a map of the cosmic microwave background. The estimator is optimized for primordial non-Gaussianity detection, but can also be useful in distinguishing primordial non-Gaussianity from secondary non-Gaussianity, such as may arise from unsubtracted point sources, or residuals from component separation. Extending earlier studies we present unbiased non-Gaussianity estimators optimized for partial sky coverage and inhomogeneous noise associated with realistic scan strategies, but which retain the ability to assess foreground contamination. [ABSTRACT FROM AUTHOR]

We investigate the impact of both slow and fast polarization modulation strategies on the science return of upcoming ground-based experiments aimed at measuring the B-mode polarization of the cosmic microwave background. Using detailed simulations of the OVER experiment, we compare the ability of modulated and un-modulated observations to recover the signature of gravitational waves in the polarized CMB sky in the presence of a number of anticipated systematic effects. The general expectations that fast modulation is helpful in mitigating low-frequency detector noise, and that the additional redundancy in the projection of the instrument's polarization sensitivity directions on to the sky when modulating reduces the impact of instrumental polarization, particularly for fast modulation, are borne out by our simulations. Neither low-frequency polarized atmospheric fluctuations nor systematic errors in the polarization sensitivity directions are mitigated by modulation. Additionally, we find no significant reduction in the effect of pointing errors by modulation. For a OVER-like experiment, pointing jitter should be negligible but any systematic miscalibration of the polarization coordinate reference system results in significant E– B mixing on all angular scales and will require careful control. We also stress the importance of combining data from multiple detectors in order to remove the effects of common-mode systematics (such as un-polarized atmospheric noise) on the measured polarization signal. Finally we compare the performance of our simulated experiment with the predicted performance from a Fisher analysis. We find good agreement between the (optimal) Fisher predictions and the simulated experiment except for the very largest scales where the power spectrum estimator we have used introduces additional variance to the B-mode signal recovered from our simulations. In terms of detecting the total B-mode signal, including lensing, the Fisher analysis and the simulations are in excellent agreement. For a detection of the primordial B-mode signal only, using an input tensor-to-scalar ratio of , the Fisher analysis predictions are ∼20 per cent better than the simulated performance. [ABSTRACT FROM AUTHOR]

We consider the shape of the likelihood and posterior surfaces to be used when fitting cosmological models to cosmic microwave background (CMB) temperature and polarization power spectra measured from experiments. In the limit of an all-sky survey with Gaussian-distributed pixel noise we show that the true combined likelihood of the four CMB power spectra (TT, TE, EE and BB) has a Wishart distribution and we discuss the properties of this function. We compare various fits to the posterior surface of the Cl values, both in the case of a single auto-power spectrum and for a combination of temperature and polarization data. In the latter case, it is important that the fits can accurately match the Wishart distribution in the limit of near full-sky coverage. Simple extensions of auto-power spectrum fits to include polarization data generally fail to match correlations between the different power spectra in this limit. Directly fitting pixel values on large scales, as undertaken by the Wilkinson Microwave Anisotropy Probe team in their analysis of the 3-yr data, avoids the complications of characterizing the shape of the posterior for the power spectra. Finally, we demonstrate the importance of the likelihood distribution on analytic marginalization, and provide a formula for analytic marginalization over a calibration error given an all-sky survey. [ABSTRACT FROM AUTHOR]