The bias of the log power spectrum for discrete surveys. (12th December 2017) - Repp, Andrew; Szapudi, István
Abstract: A primary goal of galaxy surveys is to tighten constraints on cosmological parameters, and the power spectrum P ( k ) is the standard means of doing so. However, at translinear scales P ( k ) is blind to much of these surveys' information – information which the log density power spectrum recovers. For discrete fields (such as the galaxy density), A * denotes the statistic analogous to the log density: A * is a 'sufficient statistic' in that its power spectrum (and mean) capture virtually all of a discrete survey's information. However, the power spectrum of A * is biased with respect to the corresponding log spectrum for continuous fields, and to use $P_{A^*}(k)$ to constrain the values of cosmological parameters, we require some means of predicting this bias. Here, we present a prescription for doing so; for Euclid -like surveys (with cubical cells 16 h −1  Mpc across) our bias prescription's error is less than 3 per cent. This prediction will facilitate optimal utilization of the information in future galaxy surveys.