 Vacuum prescription for inflationary in-in integrals

The Gaussian Bunch-Davies vacuum is selected by tilting the early endpoint to $-\infty (1-i\epsilon )$ for integrands $e^{iK\tau }$ with $K>0$. They then decay at the early boundary. The complex-conjugate integrand requires the opposite tilt. Ordered contractions and their contour must be conjugated together.