Infrared dynamics in de Sitter space from Schwinger–Dyson equations

Abstract

We study the two-point correlator of an O(N) scalar field with quartic self-coupling in de Sitter space. For light fields in units of the expansion rate, perturbation theory is plagued by large logarithmic terms for superhorizon momenta. We show that a proper treatment of the infinite series of self-energy insertions through the Schwinger-Dyson equations resums these infrared logarithms into power laws. We provide an exact analytical solution of the Schwinger-Dyson equations for infrared momenta when the self-energy is computed at two-loop order. Our findings encompass previously obtained results using either stochastic or Euclidean approaches. The obtained correlator exhibits a rich structure with a superposition of free-field-like power laws. We extract mass and field-strength renormalization factors from the asymptotic infrared behavior. The latter are nonperturbative in the coupling in the case of a vanishing tree-level mass.

O(N) model in Euclidean de Sitter space: beyond the leading infrared approximation

“…For example, recently, it has been shown that the stochastic and the in-in Lorentzian calculations are equivalent at the level of Feynman rules for massive fields, when computing equal-time correlation functions in the leading IR approximation [21], in agreement with previous arguments [22]. The evaluation of the field variance in the large N limit gives the same result in the three approaches, up to next to leading order (NLO) in 1/N , in the IR limit [15,16]. The connection between the Feynman diagrams for computing correlation functions in the in-in formalism and the analytically continued ones obtained in the Euclidean space has been described in detail in [23,24] for massive fields.…”

“…We will also show that the corrections of order 1/N of our result coincide in the leading IR approximation with the ones of refs. [15,16], which are the most precise results known so far for this model and were obtained working in the leading IR approximation and directly in the framework of the QFT in Lorentzian spacetime. Our results improve on those by including systematically the corrections coming from the interactions of both IR and UV sectors.…”

“…However, in refs. [15,16] the authors were able to obtain results up to the NLO in the 1/N expansion which are valid at the leading order in the IR. We refer the reader to their paper for JHEP09(2016)117 the details.…”

“…Other approaches consider the analysis of the Schwinger-Dyson equations (or their nonequilibrium counterpart, the Kadanoff-Baym equations), combined with a separation of long and short wavelengths using a physical momentum decomposition [15,16]. There are also calculations based on the dynamical renormalization group, and on the exact renormalization group equation for the effective potential [17,18].…”

“…In this approximation, the authors have obtained a self-consistent solution of the Schwinger-Dyson equations for the IR two-point functions that is valid at NLO in 1/N and at leading order in the IR. In particular, the result for the dynamical mass can be written as [15,16]: 16) where the dots stand for corrections that are higher order in either √ λ or 1/N (which cannot be unambiguously computed in the approximation considered, since they depend on the arbitrary IR scale µ IR ). Clearly, this result agrees with our eq.…”