Arguments against using $h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$ 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 $8h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$, ${\sigma }_8$. 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 $h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$ 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 $12\mathrm{M}\mathrm{p}\mathrm{c}$, whose value is similar to the standard ${\sigma }_8$ for $h\sim 0.67$.