De Sitter curvature mode function ($u_k(\tau )$)

For approximately constant $H$ and $ϵ$, a vacuum-normalized curvature mode is $u_k(\tau )=H(1+ik\tau )e^{-ik\tau }/\sqrt{4ϵM_{\mathrm{Pl}}^2{k}^3}$. Its derivative is $u_k^{\prime }=H{k}^2\tau e^{-ik\tau }/\sqrt{4ϵM_{\mathrm{Pl}}^2{k}^3}$. Ordered unequal-time Wick contractions use the complex conjugate at the earlier vertex, consistently with the vacuum prescription for inflationary in-in integrals.