= Dimensional and dimensionless matter spectra across equality
{title2=$\mathscr P(k)=k^3P(k)/(2\pi^2)$}
The dimensionless spectrum is $\mathscr P(k)=k^3P(k)/(2\pi^2)$. If it rises as $k^4$ below equality and as $\ln^2k$ above equality, then the dimensional spectrum rises as $k$ and falls as $k^{-3}\ln^2k$. Thus the dimensional spectrum has a turnover while the dimensionless spectrum only bends to a much slower rise. A schematic transition must smoothly join the two asymptotic regimes.
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