Massive stochastic Schwinger production in de Sitter

Determine the full massive de Sitter noise kernel and characterize its relation to the non-perturbative constant-field Schwinger result, including the dependence on the fermion mass, spacetime curvature, and the ratio of the mass to the Hubble scale.

Background

The paper derives the stochastic Schwinger effect for massless conformal matter, for which conformal invariance maps the fermionic dynamics in de Sitter spacetime to the flat-space problem. This allows the authors to obtain an analytically tractable noise kernel that is independent of the Hubble scale at leading order.

The authors explain that this simplification fails for massive QED: massive fermions are not conformally invariant, their mode functions are no longer plane waves, and the stochastic noise kernel acquires genuine dependence on both the mass-to-Hubble ratio and spacetime curvature. Consequently, the massless comparison between the soft stochastic limit and the non-perturbative constant-field Schwinger result cannot be straightforwardly generalized to massive matter. The unresolved task is therefore to compute the massive de Sitter noise kernel and use it to compare perturbative stochastic production with the non-perturbative constant-field result.

References

For $m\neq0$, however, the comparison is less direct. Already in flat spacetime the quadratic kernel develops the pair-production threshold $\sqrt{-K2}\ \geq\ 2m$, while in de Sitter the corresponding massive stochastic kernel is considerably more involved: massive QED is not conformally invariant, the fermion modes are no longer plane waves, and the kernel acquires genuine dependence on $m/H$ and on the spacetime curvature. Consequently, the simple massless comparison between the soft stochastic limit and the constant-field result does not carry over in any straightforward way. A proper comparison therefore requires the full massive de Sitter noise kernel, which we do not compute here. We leave the detailed analysis of the massive stochastic regime and its relation to the non-perturbative constant-field Schwinger result for future work.

— Stochastic Schwinger Effect: de Sitter and beyond  (2608.19378 - García-Consuegra et al., 19 Aug 2026) in Section 3.3, “Long-wavelength limit and connection to static Schwinger effect” (subsection label: sec:constant_field_limit)