Renormalization group inspired autonomous equations for secular effects in de Sitter space

Abstract

We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The exact solutions of these equations are free of secular terms and approach a finite limit at late times. This technique is illustrated for the well-known problem of secular growth of correlation functions of a massless scalar field with a quartic self-interaction in de Sitter space. For the expectation value of the product of two fields at coinciding space-time points we obtain a finite late-time result that is very close to the one following from Starobinsky's stochastic approach.

20 pages

References in corpus (21)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Quantum Contributions to Cosmological Correlations
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• The Trans-Planckian Problem of Inflationary Cosmology
• The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
• Super-Acceleration from Massless, Minimally Coupled ${\varphi }^4$
• Stochastic Quantum Gravitational Inflation
• On Loops in Inflation
• Super-Hubble de Sitter Fluctuations and the Dynamical RG
• Stochastic Inflationary Scalar Electrodynamics
• Two Loop Scalar Self-Mass during Inflation
• Robustness of the inflationary perturbation spectrum to trans-Planckian physics
• Trans-Planckian Issues for Inflationary Cosmology
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• Characters of different secular effects in various patches of de Sitter space
• Bogoliubov Renormalization Group and Symmetry of Solution in Mathematical Physics
• Renormalization of initial conditions and the trans-Planckian problem of inflation
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Cosmological UV/IR Divergences and de-Sitter Spacetime
• The quantum Fokker-Planck equation of stochastic inflation

Cited by in corpus (9)

• Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach
• Observations in Quantum Cosmology
• Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach
• IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation
• Non-perturbative analysis for a massless minimal quantum scalar with $V(\varphi )=\lambda {\varphi }^4/4!+\beta {\varphi }^3/3!$ in the inflationary de Sitter spacetime
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• When tadpoles matter: One-loop corrections for spectator Higgs in inflation
• Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime
• From the Fokker-Planck equation to perturbative QFT's results in de Sitter space