Fermionic S-matrix and cosmological correlators: T-violation at O(H)

We study the Bunch-Davies (BD) and Unruh-de Witt (UdW) de Sitter S-matrices in the presence of spin-$1/2$ fermions. Building on recent work, this enables us to correlate the de Sitter S-matrix with cosmological correlators. We consider a finite-time version of the UdW S-matrix to study $O(H)$ corrections to some typical particle physics processes such as beta decay. Owing to the lack of time-reversal symmetry in the expanding Poincar\'e patch, we find signatures of intrinsic T-violation in polarized beta decay. The observable we study begins at $O(H)$. The possibility of T-violation was examined theoretically in the 1950's by Jackson, Treiman, and Wyld in flat space and has been probed more recently in the emiT experiment, with the purpose of examining fundamental T-violation coming from additional interactions in the Lagrangian. Our analysis places a lower bound on the intrinsic T-violation in the expanding Poincar\'e patch. At $O(H)$, we find both energy conserving and energy non-conserving contributions. Surprisingly, the energy-violating piece, in principle, can give large T-violation at fine-tuned values of the kinematical variables.