= Potential fluctuations per logarithmic wavenumber
{title2=$\Delta_\varphi^2(k)=(4\pi Ga^2\bar\rho)^2Ak^{n-1}/(2\pi^2)$}
For $P_\delta(k)=Ak^n$, the <cosmological Poisson equation> gives $P_\varphi(k)=(4\pi Ga^2\bar\rho)^2P_\delta(k)/k^4$. The contribution to variance per logarithmic <wavenumber> is $k^3P_\varphi(k)/(2\pi^2)$, giving the displayed expression and rms scaling $\varphi_{\rm rms}(R)\propto R^{(1-n)/2}$ for a band around $k\sim R^{-1}$. The <Harrison-Zeldovich spectrum> $n=1$ has equal potential variance per logarithmic interval. An uncut power law over all scales has divergent total potential variance for every $n$, so the scale-local amplitude must not be confused with a finite global rms.
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