What is required to accurately determine the physical distance to an object with a very high redshift ($z$)?

Answer

Employing the full set of Friedmann equations incorporating matter ($ ext{Ω}_m$) and dark energy ($ ext{Ω}_{ ext{Λ}}$) densities.

Converting a large expansion factor ($z$) into a precise physical distance requires a complete cosmological model, specifically the Friedmann equations, which account for the changing expansion rate dictated by the universe's composition.

What is required to accurately determine the physical distance to an object with a very high redshift ($z$)?
DistancecosmologyObjectredshift