Snowmass2021 - Letter of interest cosmology intertwined IV: The age of the universe and its curvature

A precise measurement of the curvature Universe is prime importance for cosmology since it could not only confirm paradigm primordial inflation but also help in discriminating between different early-Universe scenarios. Recent observations, while broadly consistent with a spatially flat standard ? Cold Dark Matter (?CDM) model, show tensions that still allow (and, some cases, even suggest) few percent deviations from universe. In particular, Planck Cosmic Microwave Background power spectra, assuming nominal likelihood, prefer closed universe at more than 99% confidence level. While new physics be play, this anomaly may result an unresolved systematic error or just statistical fluctuation. However, positive allows larger age Universe, accurate determination oldest objects provides smoking gun confirming falsifying current ?CDM model.