Uncertain Times: The Redshift-Time Relation from Cosmology and Stars

Abstract: Planck data provide precise constraints on cosmological parameters when assuming the base $\Lambda$CDM model, including a $0.17\%$ measurement of the age of the Universe, $t_0=13.797 \pm 0.023\,{\rm Gyr}$. However, the persistence of the "Hubble tension" calls the base $\Lambda$CDM model's completeness into question and has spurred interest in models such as Early Dark Energy (EDE) that modify the assumed expansion history of the Universe. We investigate the effect of EDE on the redshift-time relation $z \leftrightarrow t$ and find that it differs from the base $\Lambda$CDM model by at least ${\approx} 4\%$ at all $t$ and $z$. As long as EDE remains observationally viable, any inferred $t \leftarrow z$ or $z \leftarrow t$ quoted to a higher level of precision do not reflect the current status of our understanding of cosmology. This uncertainty has important astrophysical implications: the reionization epoch - $10>z>6$ - corresponds to disjoint lookback time periods in the base $\Lambda$CDM and EDE models, and the EDE value of $t_0=13.25 \pm 0.17~{\rm Gyr}$ is in tension with published ages of some stars, star clusters, and ultra-faint dwarf galaxies. However, most published stellar ages do not include an uncertainty in accuracy (due to, e.g., uncertain distances and stellar physics) that is estimated to be $\sim7-10\%$, potentially reconciling stellar ages with $t_{0,\rm EDE}$. We discuss how the big data era for stars is providing extremely precise ages ($<1\%$) and how improved distances and treatment of stellar physics such as convection could result in ages accurate to $4-5\%$, comparable to the current accuracy of $t \leftrightarrow z$. Such precise and accurate stellar ages can provide detailed insight into the high-redshift Universe independent of a cosmological model.