 Subhorizon vacuum contribution to a de Sitter scalar spectrum

The equal-time two-point function of a de Sitter scalar has a contribution $P_{\mathrm{vac}}=1/(2k{a}^2)$, 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.