Numerical simulation of non-Markovian vacuum-bubble dynamics

Develop numerical simulations of cosmological vacuum-bubble nucleation and expansion using the spatially extended Schwinger–Keldysh Langevin equation with non-Markovian memory kernels and temporally correlated non-Gaussian noise.

Background

The paper proposes relaxing the zero-mode scale split by allowing the mean field to include low-momentum spatial modes. This produces a semi-classical field equation containing spatial gradients, a non-local memory kernel, and stochastic noise, potentially enabling simultaneous treatment of vacuum-bubble nucleation and expansion.

The authors explicitly identify numerical implementation as unresolved because the memory kernel is non-Markovian and the noise has non-trivial temporal correlations. They leave the development of such simulations for future work.

References

This provides a semi-classical tool to simulate the vacuum bubble nucleation and expansion simultaneously. However, the presence of non-Markov effect in the memory kernel and the non-trivial temporal correlations of the noises may bring challenges to such a numerical simulation, which is left for future studies.

— Cosmological Vacuum Decays from Schwinger-Keldysh Formalism  (2608.12736 - Yuwen, 13 Aug 2026) in Section 5, Conclusions and Discussions