= Logarithmic high-wavenumber density-spectrum transfer
{title2=$\mathscr P_c\propto(\tau/\tau_{\rm eq})^4\ln^2(k\tau_{\rm eq})$}
A scale-invariant curvature seed gives wavenumber-independent dimensionless matter power at radiation-era horizon entry. Horizon entry at $\tau_h\sim1/k$, followed by logarithmic growth to equality, gives a density transfer proportional to $\ln(k\tau_{\rm eq})$. Subsequent matter-era growth is proportional to $\tau^2$, so the dimensionless density power is proportional to $(\tau/\tau_{\rm eq})^4\ln^2(k\tau_{\rm eq})$. This is a high-wavenumber asymptote, not an expression at the transition point.
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