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

Evidence for a high-z ISW signal from supervoids in the distribution of eBOSS quasars

The late-time integrated Sachs-Wolfe (ISW) imprint of $R\gtrsim 100~h^{-1}{\rm Mpc}$ super-structures is sourced by evolving large-scale potentials due to a dominant dark energy component in the $\Lambda$CDM model. The aspect that makes the ISW effect distinctly interesting is the repeated observation of stronger-than-expected imprints from supervoids at $z\lesssim0.9$. Here we analyze the un-probed key redshift range $0.8<z<2.2$ where the ISW signal is expected to fade in $\Lambda$CDM, due to a weakening dark energy component, and eventually become consistent with zero in the matter dominated epoch. On the contrary, alternative cosmological models, proposed to explain the excess low-$z$ ISW signals, predicted a sign-change in the ISW effect at $z\approx1.5$ due to the possible growth of large-scale potentials that is absent in the standard model. To discriminate, we estimated the high-$z$ $\Lambda$CDM ISW signal using the Millennium XXL mock catalogue, and compared it to our measurements from about 800 supervoids identified in the eBOSS DR16 quasar catalogue. At $0.8<z<1.2$, we found an excess ISW signal with $A_\mathrm{ ISW}\approx3.6\pm2.1$ amplitude. The signal is then consistent with the $\Lambda$CDM expectation ($A_\mathrm{ ISW}=1$) at $1.2<z<1.5$ where the standard and alternative models predict similar amplitudes. Most interestingly, we also detected an opposite-sign ISW signal at $1.5<z<2.2$ that is in $2.7\sigma$ tension with the $\Lambda$CDM prediction. Taken at face value, these moderately significant detections of ISW anomalies suggest an alternative growth rate of structure in low-density environments at $\sim100~h^{-1}{\rm Mpc}$ scales.Comment: 12 pages, 9 figures, submitted to MNRA