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