On the analytic continuation and asymptotic behaviour of the two-point function in massless ${\phi }^4$-theory in Euclidean de Sitter space

For the two-point function of the massless, minimally-coupled, real scalar field in Euclidean de Sitter space with $\lambda {\phi }^4$-interaction, we compute the leading-logarithmic terms in the invariant distance of the two-point function to $O({\lambda }^2)$, which counts as the fifth subleading order (N${}^5$LO) in the $\sqrt{\lambda }$-expansion. We show that the analytic continuation to Lorentzian signature coincides with the expansion of the analogous quantity computed in the stochastic formalism. We determine the large-order behaviour of the stochastic series expansion and prove its Borel summability, which suggests that the Euclidean theory can be used to extract the late-time behaviour of massless correlation functions in Lorentzian de Sitter space.