Optimally Mapping Large-scale Structures with Luminous Sources

Intensity mapping has emerged as a promising tool to probe the three-dimensional structure of the universe. The traditional approach of galaxy redshift surveys is based on individual galaxy detection, typically performed by thresholding and digitizing large-scale intensity maps. By contrast, intensity mapping uses the integrated emission from all sources in a 3D pixel (or voxel) as an analog tracer of large-scale structure. In this work, we develop a formalism to quantify the performance of both approaches when measuring large-scale structures. We compute the Fisher information of an arbitrary observable, derive the optimal estimator, and study its performance as a function of source luminosity function, survey resolution, instrument sensitivity, and other survey parameters. We identify regimes where each approach is advantageous and discuss optimal strategies for different scenarios. To determine the best strategy for any given survey, we develop a metric that is easy to compute from the source luminosity function and the survey sensitivity, and we demonstrate the application with several planned intensity mapping surveys.