= Harrison-Peebles-Zeldovich spectrum
{c}
{title2=$P(k,\tau)\propto\tau^4 k$}
= HPZ spectrum
{c}
{synonym}
= Harrison-Zeldovich spectrum
{c}
{synonym}
The Harrison-Peebles-Zeldovich spectrum is the scale-invariant primordial growing-mode spectrum: in a fixed <conformal time> slice before <cosmological horizon crossing>, the <matter power spectrum> is proportional to $\tau^4k$ in the usual growing-mode density convention. At horizon entry $\tau_H\sim k^{-1}$, its dimensionless mass <variance> $k^3P(k,\tau_H)$ is independent of $k$. This statement fixes a spectral shape, not its amplitude. <Radiation domination> subsequently suppresses small-scale density growth through the <Mészáros effect>, producing the asymptotic <matter power spectrum> $P\propto k^{-3}\ln^2(k/k_{\rm eq})$ after <matter-radiation equality>.
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