= Subhorizon vacuum contribution to a de Sitter scalar spectrum
{title2=$\Delta^2_{\rm vac}(k,\tau)=k^2/(4\pi^2a^2)$}
= Subhorizon vacuum contribution
{synonym}
The <equal-time two-point function of a de Sitter scalar> has a contribution $P_{\rm vac}=1/(2ka^2)$, giving the displayed dimensionless <power spectrum> per logarithmic <wavenumber>. At fixed comoving <wavenumber> it decreases as $a^{-2}$; on short physical scales it reproduces the vacuum fluctuations of a <massless scalar field> in <Minkowski spacetime>. Its coincident integral is ultraviolet divergent, so the fixed-mode decrease cannot be interchanged with an unregulated integral over all modes.
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