Unveiling the cosmological information beyond linear scales: forecasts for sufficient statistics

Beyond the linear regime, Fourier modes of cosmological random fields become correlated, and the power spectrum of density fluctuations contains only a fraction of the available cosmological information. To unveil this formerly hidden information, the A* non-linear transform was introduced; it is optimized both for the nonlinearities induced by gravity and observational noise. Quantifying the resulting increase of our knowledge of cosmological parameters, we forecast the constraints from the angular power spectrum and that of A* from l ~ 200 to 3000 for upcoming galaxy surveys such as: the Wide-Field Infrared Survey Telescope (WFIRST), the Large Synoptic Survey Telescope (LSST), Euclid, the Hyper Suprime-Cam (HSC) and the Dark Energy Survey (DES). We find that at low redshifts this new data analysis strategy can double the extracted information, effectively doubling the survey area. To test the accuracy of our forecasting and the power of our data analysis methods, we apply the A* transformation to the latest release of the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) Wide. While this data set is too sparse to allow for more than modest gains (~1.1-1.2), the realized gain from our method is in excellent agreement with our forecast, thus verifying the robustness of our analysis and prediction pipelines.Comment: 11, 7 figures, 6 table

Fast Edge Corrected Measurement of the Two-Point Correlation Function and the Power Spectrum

We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point function with an heuristically weighted edge corrected estimator. Once the correlation function is measured, we estimate the power spectrum via numerical integration of the Hankel transform connecting the two. We introduce an efficient numerical technique based on Gauss-Bessel-quadrature and double exponential transformation. This, combined with our, or any similar, two-point function estimator leads to a novel edge corrected estimator for power spectra. The pair of techniques presented are the Euclidean analogs of those developed and widely used in cosmic microwave background research for spherical maps.Comment: 4 pages, 2 figures, submitted to ApJ

Effects of Sampling on Statistics of Large Scale Structure

The effects of sampling are investigated on measurements of counts-in-cells in three-dimensional magnitude limited galaxy surveys, with emphasis on moments of the underlying smooth galaxy density field convolved with a spherical window. A new estimator is proposed for measuring the k-th order moment < rho^k >: the weighted factorial moment F_k[w], corrected for the effects of the varying selection function. The cosmic error on the measurement of F_k[w] is computed via the the formalism of Szapudi & Colombi (1996), which is generalized to include selection effects. The integral equation for finding the minimum variance weight is solved numerically, and an intuitive analytical approximation is derived. The resulting estimator is more accurate than the traditional method of counts-in-cells in volume limited samples, which discards useful information. As a practical example we consider the case of the future Sloan Digital Sky Survey. Optimal (sparse) sampling strategies for designing magnitude limited redshift surveys are investigated as well. It is found that the optimal strategy depends greatly on the statistics and scales considered. Finally we consider the issue of designing the geometry of a catalog, when it covers only a small fraction of the sky.Comment: 24 pages, 9 figures, Latex (MN format), accepted for publication in MNRA