To the sphere and back again: de Sitter infrared correlators at NTLO in 1/N

We analyze the infrared behavior of the two and four-point functions for the massless $O(N)$ model in Lorentzian de Sitter spacetime, using the $1\mathrm{/}N$ expansion. Our approach is based in the study of the Schwinger-Dyson equations on the sphere (Euclidean de Sitter space), using the fact that the infrared behavior in Lorentzian spacetime is determined by the pole structure of the Euclidean correlation functions. We compute the two-point function up to the NTLO in $1\mathrm{/}N$, and show that in the infrared it behaves as the superposition of two massive free propagators with effective masses of the same order, but not equal to, the dynamical mass $m_{dyn}$. We compare our results with those obtained using other approaches, and find that they are equivalent but retrieved in a considerably simpler way. We also discuss the infrared behavior of the equal-times four-point functions.