= Eight-megaparsec density fluctuation amplitude
{title2=$\sigma_8$}
= Sigma eight
{synonym}
The parameter $\sigma_8$ is the present linear rms <density contrast> averaged in a spherical top-hat of comoving radius $8h^{-1}\,\mathrm{Mpc}$, with $h=H_0/(100\,\mathrm{km\,s^{-1}\,Mpc^{-1}})$. Thus $\sigma_8^2=(2\pi^2)^{-1}\int_0^\infty k^2P_m(k,0)|W(kR_8)|^2\,dk$. It specifies an amplitude on a chosen scale rather than the complete <matter power spectrum>; converting cluster abundance into this parameter also requires a spectral shape and background cosmology.
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