Effective Action and Gravitational Pair Production in (A)dS Spacetime

We compute the effective action for a massive scalar field in (A)dS spacetime using the Euclidean heat kernel method. We highlight that in even-dimensional dS spacetimes, the effective action exhibits a non-trivial imaginary part, reminiscent of the Schwinger effect in quantum electrodynamics. We find consistency between the results obtained from the Euclidean heat kernel method with those from the Green's function approach in Lorentzian signature. Additionally, we compare our results with the perturbative calculations and find that the perturbation theory almost fails to capture the correct non-perturbative imaginary part of the effective action. This discrepancy presents a challenge to computing the gravitational pair production using the perturbation theory.