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

Abstract

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 $1/N$ 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 $1/N$, 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.

arXiv comment10 pages, 1 figure

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• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Unequal time correlators of stochastic scalar fields in de Sitter space
• The $1/N$ expansion for stochastic fields in de Sitter spacetime
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Novel mechanism for CMB modulation in the Standard Model
• Quantum backreaction of $O(N)$-symmetric scalar fields and de Sitter spacetimes at the renormalization point: renormalization schemes and the screening of the cosmological constant