Cosmological Distance Indicators

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time-delays from strongly lensed quasars currently provide constraints on H₀ with < 4 % uncertainty, and with 1 % within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to z≲ 0.8 with galaxies and z∼ 2 with Ly-α forest, providing precise distance measurements and H₀ with < 2 % uncertainty in flat Λ CDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at z∼ 0.8 and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach 1 % uncertainty in determining H₀, to assess the current tension in H₀ measurements that could indicate new physics.