Cluster Assembly Times as a Cosmological Test
  The abundance of galaxy clusters in the low-redshift universe provides an
important cosmological test, constraining a product of the initial amplitude of
fluctuations and the amount by which they have grown since early times. The
degeneracy of the test with respect to these two factors remains a limitation
of abundance studies. Clusters will have different mean assembly times,
however, depending on the relative importance of initial fluctuation amplitude
and subsequent growth. Thus, structural probes of cluster age such as
concentration, shape or substructure may provide a new cosmological test that
breaks the main degeneracy in number counts. We review analytic predictions for
how mean assembly time should depend on cosmological parameters, and test these
predictions using cosmological simulations. Given the overall sensitivity
expected, we estimate the cosmological parameter constraints that could be
derived from the cluster catalogues of forthcoming surveys such as Euclid, the
Nancy Grace Roman Space Telescope, eROSITA, or CMB-S4. We show that by
considering the structural properties of their cluster samples, such surveys
could easily achieve errors of $\Delta \sigma_8$ = 0.01 or better.
