Cosmological Correlators from Resurgence

Abstract

Integrating out heavy particles is generally viewed as an irreversible procedure that erases some physical information above the cutoff scale of the resulting effective theory. However, this does not preclude the possibility of recovering the heavy propagating degrees from the low-energy effective theory with appropriate boundary data supplied. A classic example is the recovery of Schwinger pair production from the resummed Euler-Heisenberg effective action. In this work, we perform a similar exercise in a cosmological setting. We show that it is possible to reconstruct the inflationary correlators with massive exchanges, for a discrete heavy spectrum and arbitrary tree topologies, from the low-energy effective theory together with unitarity and Bunch-Davies boundary conditions. The divergent EFT series is resummed in three ways: the boundary differential operators, spectral representation, and Borel resummation, and the exponentially suppressed cosmological collider signals are recovered via analytic continuation. Our construction provides a resurgent relation between the local EFT background and the nonanalytic heavy-particle production, and may also be viewed as an inverse problem for the dispersive bootstrap.