Arguments against using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mtext> </mml:mtext><mml:mi>Mpc</mml:mi></mml:mrow></mml:math> units in observational cosmology
Ariel G. Sánchez
Abstract
It is common to express cosmological measurements in units of ${h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}$. 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 $8\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$, ${\ensuremath{\sigma}}_{8}$. This parameter does not correctly capture the impact of $h$ on the amplitude of density fluctuations. We show that the use of ${\ensuremath{\sigma}}_{8}$ has caused critical misconceptions for both the so-called ${\ensuremath{\sigma}}_{8}$ 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 ${h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}$ units in cosmology and to characterize the amplitude of the matter power spectrum in terms of ${\ensuremath{\sigma}}_{12}$, defined as the mass fluctuation in spheres of radius 12 Mpc, whose value is similar to the standard ${\ensuremath{\sigma}}_{8}$ for $h\ensuremath{\sim}0.67$.