Measuring $H_0$ with Spectroscopic Surveys

Abstract

Galaxy surveys map the three-dimensional distribution of matter in the Universe, encoding information about both the primordial cosmos and its subsequent evolution. By comparing the angular and physical scales of features in the galaxy distribution, we can compute the physical distance to the sample, and thus extract the Hubble parameter, $H_0$. In this chapter, we discuss how this is performed in practice, introducing two key ``standard rulers''. The first, the sound horizon at recombination, leads to baryon acoustic oscillations, and, by combining with external data from the CMB or Big Bang Nucleosynthesis, leads to a competitive $H_0$ constraint. Information can also be extracted from the physical scale of the horizon at matter-radiation equality; though somewhat less constraining, this depends on very different physics and is an important validation test of the physical model. We discuss how both such constraints can be derived (using ``template'' and ``full-shape'' methodologies), and present a number of recent constraints from the literature, some of which are comparable in precision to (and independent from) Planck. Finally, we discuss future prospects for improving these constraints in the future.