De Sitter diagrammar and the resummation of time

Matthew Baumgart, Raman Sundrum

Research output: Contribution to journalArticlepeer-review

30 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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