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 ΛCDM. 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.Comment: Review article accepted for publication in Space Science Reviews
(Springer), 45 pages, 10 figures. Chapter of a special collection resulting
from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in
the Space Ag