It looks like we might be able to measure distances using quasars – the very bright, distant objects which are the result of supermassive black holes consuming matter in early galaxies. The key is the relationship between how bright they are in ultraviolet light compared to X-rays:
They found that the tight correlation already known to exist between the ultraviolet and X-ray luminosity of local quasars continues in distant quasars, back over 85% of the age of the Universe, becoming even tighter at earlier times.Quasars as Cosmic Standard Candles, Harvard Center for Astrophysics
This can allow the distance to the quasars to be estimated by measuring what’s known as dispersion. That’s the difference in how long it takes the UV and X-ray light to reach us. Different wavelengths of light are affected differently by travelling through different materials, so some wavelengths travel more slowly through some materials.
It turns out that the dispersion seen in UV and X-rays from quasars mostly comes from the intergalactic medium (rather than things like dust surrounding the source). That’s great news! It means that we can estimate the distance of quasars just by observing them in UV and X-rays. That makes it easier to study quasars themselves, and also potentially gives us a new, independent way of measuring the expansion of the Universe.