De Sitter diagrammar and the resummation of time

Matthew Baumgart, Raman Sundrum

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy “landscape” on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momen- tum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the “Stochastic Inflation” ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.

Original languageEnglish (US)
Article number119
JournalJournal of High Energy Physics
Issue number7
StatePublished - Jul 1 2020


  • Cosmology of Theories beyond the SM
  • Effective Field Theories
  • Renormalization Group

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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