Arguments against using $h^{-1}{\rm Mpc}$ units in observational
  cosmology
  It is common to express cosmological measurements in units of $h^{-1}{\rm
Mpc}$. Here, we review some of the complications that originate from this
practice. A crucial problem caused by these units is related to the
normalization of the matter power spectrum, which is commonly characterized in
terms of the linear-theory rms mass fluctuation in spheres of radius
$8\,h^{-1}{\rm Mpc}$, $\sigma_8$. This parameter does not correctly capture the
impact of $h$ on the amplitude of density fluctuations. We show that the use of
$\sigma_8$ has caused critical misconceptions for both the so-called $\sigma_8$
tension regarding the consistency between low-redshift probes and cosmic
microwave background data, and the way in which growth-rate estimates inferred
from redshift-space distortions are commonly expressed. We propose to abandon
the use of $h^{-1}{\rm Mpc}$ units in cosmology and to characterize the
amplitude of the matter power spectrum in terms of $\sigma_{12}$, defined as
the mass fluctuation in spheres of radius $12\,{\rm Mpc}$, whose value is
similar to the standard $\sigma_8$ for $h\sim 0.67$.
