Measuring the Hubble Constant Near and Far in the Era of ELT's

Many of the fundamental physical constants in Physics, as a discipline, are measured to exquisite levels of precision. The fundamental constants that define Cosmology, however, are largely determined via a handful of independent techniques that are applied to even fewer datasets. The history of the measurement of the Hubble Constant (H0), which serves to anchor the expansion history of the Universe to its current value, is an exemplar of the difficulties of cosmological measurement; indeed, as we approach the centennial of its first measurement, the quest for H0 still consumes a great number of resources. In this white paper, we demonstrate how the approaching era of Extremely Large Telescopes (ELTs) will transform the astrophysical measure of H0 from the limited and few into a fundamentally new regime where (i) multiple, independent techniques are employed with modest use of large aperture facilities and (ii) 1% or better precision is readily attainable. This quantum leap in how we approach H0 is due to the unparalleled sensitivity and spatial resolution of ELT's and the ability to use integral field observations for simultaneous spectroscopy and photometry, which together permit both familiar and new techniques to effectively by-pass the conventional 'ladder' framework to minimize total uncertainty. Three independent techniques are discussed -- (i) standard candles via a two-step distance ladder applied to metal, poor stellar populations, (ii) standard clocks via gravitational lens cosmography, and (iii) standard sirens via gravitational wave sources -- each of which can reach 1% with relatively modest investment from 30-m class facilities.