Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: the ladder-rainbow approximation

Abstract

We study the infrared (large separation) behavior of a massless minimally coupled scalar quantum field theory with a quartic self interaction in de Sitter spacetime. We show that the perturbation series in the interaction strength is singular and secular, i.e. it does not lead to a uniform approximation of the solution in the infrared region. Only a nonperturbative resummation can capture the correct infrared behavior. We seek to justify this picture using the Dyson-Schwinger equations in the ladder-rainbow approximation. We are able to write down an ordinary differential equation obeyed by the two-point function and perform its asymptotic analysis. Indeed, while the perturbative series-truncated at any finite order-is growing in the infrared, the full nonperturbative sum can be decaying.

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References in corpus (17)

• De Sitter Space and Eternity
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Lecture notes on interacting quantum fields in de Sitter space
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• On the Instability of Global de Sitter Space to Particle Creation
• On the proper treatment of massless fields in Euclidean de Sitter space
• Infrared dynamics in de Sitter space from Schwinger-Dyson equations
• On "dynamical mass" generation in Euclidean de Sitter space
• Nonperturbative resummation of de Sitter infrared logarithms in the large-N limit
• Quantum Vacuum Instability of 'Eternal' de Sitter Space
• Recursive relations in the core Hopf algebra
• Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• Physical momentum representation of scalar field correlators in de Sitter space
• Infrared behavior and gauge artifacts in de Sitter spacetime: The photon field
• Generalizing Starobinskii's Formalism to Yukawa Theory & to Scalar QED
• Algebraic Structures in local QFT

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