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

TL;DR

This paper examines how alternative cosmological models like Early Dark Energy affect the redshift-time relation, revealing significant uncertainties that impact astrophysical inferences and stellar age estimates.

Contribution

It quantifies the differences in the redshift-time relation between ΛCDM and EDE models and discusses implications for stellar ages and cosmological measurements.

Findings

EDE models differ from ΛCDM by at least 4% in the redshift-time relation.

Discrepancies in cosmological models affect the inferred ages of the Universe and stars.

Precise stellar ages can help independently probe high-redshift cosmology.

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.