Have we exhausted the galaxy two-point function?

Abstract: Throughout the past three decades, the analysis of spectroscopic surveys has focussed around the two-point function of the galaxy overdensity field, masquerading either as the correlation function or the Fourier-space power spectrum. Today, theoretical interest has shifted towards other statistics, in particular the higher-point functions. Does this mean we are confident in our understanding of the power spectrum’s intricacies? In this talk, I will argue that, despite a huge wealth of previous work, two-point analyses can yet be improved. In particular, I will discuss a selection of recent works concerning power spectrum estimation and analysis, focussing on optimal power spectrum estimation and compression, faster small-scale estimators, subtleties in the definition of the anisotropic power spectra, and the question of whether we can do better using transformations of the density field. Such questions will be of great importance for upcoming large-scale structure surveys such as DESI and Euclid.