Going back to measuring distances at the largest scale, there are various new ideas being pursued for physical indicators of distance. Importantly these are independent of redshift and thus give an opportunity for calibrating methods based on redshift.
We briefly describe three of these techniques, with links for further reading.
Gravitational Lens Time Delay
One promising technique is the use of the effect of gravitational lensing of images of quasars. When we see a quasar through two different paths because of a gravitational lens, the two paths differ in length and therefore also the travel time of the light. When the quasar varies in intensity abruptly (as they do), we see that variation with a time delay in one path as compared to the other.
This time delay is a measure for the distance. This method does not yet give accurate results, primarily because the lensing effect depends on the unknown mass distribution of the lensing cluster of galaxies. When this improves this method will be an important indicator for large distances, because it is independent of any other method and thus does not require calibration like other methods in the Cosmic Distance ladder.
The large mass of a galaxy cluster including its dark matter bends passing light rays, forming an "Einstein Ring".The HST image shows parts of this ring from the blue, distant galaxy. The lensing cluster is at a distance of about 4 Gly.
The Cosmic Microwave Background radiation (CMB) is affected in certain parts of the sky by hot gas in galaxy clusters if the CMB happens to pass through. With this very difficult technique, the observed angular diameter of the galaxy cluster could be a measure for its distance. Importantly this distance is independent from redshift.
Gravitational Wave Astronomy
Since 2017 astronomers have been able to detect gravitational waves caused by merging neutron stars in a binary system. In some cases it has been possible to also measure the same event in the EM spectrum as a gamma-ray burst. The amplitude of the gravitational waves enables scientists to determine distance to this event, independently from any other technique in the distance ladder.