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We trace with analytical methods and in a model parameter-independent manner the independent bits of Fisher information of each of the moments of the lognormal distribution as a now standard prescription for the distribution of the cosmological matter density field as it departs from Gaussian initial conditions. We show that, when entering the regime of large fluctuations, only a tiny, dramatically decaying fraction of the total information content remains accessible through the extraction of the full series of moments of the field. This is due to the known peculiarity of highly tailed distributions that they cannot be uniquely recovered given the values of all of their moments. Under this lognormal assumption, cosmological probes such as the correlation function hierarchy or, equivalently, their Fourier transforms, are rendered fundamentally limited once the field becomes nonlinear, for any parameter of interest. We show that the fraction of the information accessible from two-point correlations decays to zero following the inverse squared variance of the field. We discuss what general properties of a random field's probability density function are making the correlation function hierarchy an efficient or inefficient, complete or incomplete, set of probes of any model parameter. [ABSTRACT FROM AUTHOR]

A critical challenge in the observation of the redshifted 21 cm line is its separation from bright Galactic and extragalactic foregrounds. In particular, the instrumental leakage of polarized foregrounds, which undergo significant Faraday rotation as they propagate through the interstellar medium, may harmfully contaminate the 21 cm power spectrum. We develop a formalism to describe the leakage due to instrumental widefield effects in visibility-based power spectra measured with redundant arrays, extending the delay-spectrum approach presented in Parsons et al. We construct polarized sky models and propagate them through the instrument model to simulate realistic full-sky observations with the Precision Array to Probe the Epoch of Reionization. We find that the leakage due to a population of polarized point sources is expected to be higher than diffuse Galactic polarization at any k mode for a 30 m reference baseline. For the same reference baseline, a foreground-free window at k > 0.3 h Mpc−1 can be defined in terms of leakage from diffuse Galactic polarization even under the most pessimistic assumptions. If measurements of polarized foreground power spectra or a model of polarized foregrounds are given, our method is able to predict the polarization leakage in actual 21 cm observations, potentially enabling its statistical subtraction from the measured 21 cm power spectrum. [ABSTRACT FROM AUTHOR]

A critical challenge in measuring the power spectrum of 21 cm emission from cosmic reionization is compensating for the frequency dependence of an interferometer's sampling pattern, which can cause smooth-spectrum foregrounds to appear unsmooth and degrade the separation between foregrounds and the target signal. In this paper, we present an approach to foreground removal that explicitly accounts for this frequency dependence. We apply the delay transformation introduced in Parsons & Backer to each baseline of an interferometer to concentrate smooth-spectrum foregrounds within the bounds of the maximum geometric delays physically realizable on that baseline. By focusing on delay modes that correspond to image-domain regions beyond the horizon, we show that it is possible to avoid the bulk of smooth-spectrum foregrounds. We map the point-spread function of delay modes to k-space, showing that delay modes that are uncorrupted by foregrounds also represent samples of the three-dimensional power spectrum, and can be used to constrain cosmic reionization. Because it uses only spectral smoothness to differentiate foregrounds from the targeted 21 cm signature, this per-baseline analysis approach relies on spectrally and spatially smooth instrumental responses for foreground removal. For sufficient levels of instrumental smoothness relative to the brightness of interfering foregrounds, this technique substantially reduces the level of calibration previously thought necessary to detect 21 cm reionization. As a result, this approach places fewer constraints on antenna configuration within an array, and in particular, facilitates the adoption of configurations that are optimized for power-spectrum sensitivity. Under these assumptions, we demonstrate the potential for the Precision Array for Probing the Epoch of Reionization (PAPER) to detect 21 cm reionization at an amplitude of 10 mK2 near k ∼ 0.2 h Mpc–1 with 132 dipoles in 7 months of observing. [ABSTRACT FROM AUTHOR]