Nonperturbative resummation of de Sitter infrared logarithms in the large-Nlimit

Abstract

We study the O(N ) scalar field theory with quartic self-coupling in de Sitter space. When the field is light in units of the expansion rate, perturbative methods break down at very low momenta due to large infrared logarithmic terms. Using the nonperturbative large-N limit, we compute the four-point vertex function in the deep infrared regime. The resummation of an infinite series of perturbative (bubble) diagrams leads to a modified power law which is analogous to the generation of an anomalous dimension in critical phenomena. We discuss in detail the role of high momentum (subhorizon) modes, including the issue of renormalization, and show that they influence the dynamics of infrared (superhorizon) modes only through a constant renormalization factor. This provides an explicit example of effective decoupling between high and low energy physics in an expanding space-time.

Infrared dynamics in de Sitter space from Schwinger–Dyson equations

“…The rationale here is that one expects the high momentum contribution not to bring large infrared logarithms, which we are interested in. A detailed analysis of the high momentum contribution to a similar integral equation in the calculation of the four-point function in the large-N limit has been performed in [30]. Although the details are rather subtle, the naive expectation appears correct in that case and the high momentum modes only contribute a renormalization factor of order unity.…”

“…Introducing an arbitrary scale µ 1 to separate between super and subhorizon modes, one can show, using the method developed in Ref. [30], that the dominant contribution to the momentum integral in Eq. (16) for p, p ′ µ comes from momenta qp, qp ′ , lp, lp ′ µ, which implies qr, qr ′ µ.…”

“…1 In de Sitter space, this can equivalently be seen as a mass correction [30]. The resulting two-point correlator exhibits an interesting structure with a superposition of free-fieldlike power laws.…”

“…Employing the physical momentum representation for de Sitter correlators (hereafter called the p-representation) [28,38] and the techniques developed in Ref. [30], we show that the Schwinger-Dyson equation, restricted to infrared momenta, is amenable to a one-dimensional integrodifferential equation that can be exactly solved by analytical means. Using the analysis of Ref.…”

“…In recent years, a lot of activity has been devoted to adapt these techniques to nontrivial cosmological spaces, mainly for scalar fields. These include semiclassical stochastic methods [4,19], renormalization group [20,21], two-particle-irreducible (2PI) [22-25, 27, 28], or large-N techniques [29,30], ladder-rainbow resummation [31], or a field theoretic generalization of the Wigner-Weisskopf method [32,33]. Useful information can also be gained by considering Euclidean de Sitter space [11,34,35].…”