Quantifying the uncertainty in the time-redshift relationship

Michael S. Turner

Published 2024-03-28Version 1

The age of the Universe at a given redshift is a fundamental relationship in cosmology. For many years, the uncertainties in it were dauntingly large, close to a factor of 2. In this age of precision cosmology, they are now at the percent level and dominated solely by the Hubble constant. The uncertainties due to the parameters that describe the cosmological model are must less important. In decreasing order they are: uncertainty due to the dark energy equation-of-state parameter $w$, at most 0.9%; uncertainty due to the matter density $\Omega_M$, at most 0.5% and uncertainty due to the curvature parameter $\Omega_k$, at most 0.07%.