Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space

Abstract

We consider a massive scalar field with quartic self-interaction $\lambda /4!{\varphi }^4$ in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism. For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e. to leading order in $m^2/H^2$, where $m$ is the mass of the scalar field and $H$ is the Hubble rate. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with $0\le m^2\ll \sqrt{\lambda }{H}^2$ for which the perturbation expansion fails at late times.

arXiv comment25 pages, 4 figures

References in corpus (50)

• Planck 2013 results. XVI. Cosmological parameters
• Quantum Contributions to Cosmological Correlations
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Quantum effects can render w<-1 on cosmological scales
• Keldysh technique and non-linear sigma-model: basic principles and applications
• Super-Acceleration from Massless, Minimally Coupled ${\varphi }^4$
• Quantum-to-classical transition for fluctuations in the early Universe
• Stochastic Quantum Gravitational Inflation
• Super-Hubble de Sitter Fluctuations and the Dynamical RG
• Les Houches Lectures on De Sitter Space
• Stochastic Inflationary Scalar Electrodynamics
• Infrared effects in inflationary correlation functions
• Two Loop Scalar Self-Mass during Inflation
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Photon mass from inflation
• Coarse graining and decoherence in quantum field theory
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• Stochastic growth of quantum fluctuations during slow-roll inflation
• On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
• One-loop corrections to the curvature perturbation from inflation
• One-loop corrections to a scalar field during inflation
• On Resumming Inflationary Perturbations beyond One-loop
• On the proper treatment of massless fields in Euclidean de Sitter space
• Classical approximation for time dependent quantum field theory: diagrammatic analysis for hot scalar fields
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT
• Infrared dynamics in de Sitter space from Schwinger-Dyson equations
• Effective potential for quantum scalar fields on a de Sitter geometry
• On "dynamical mass" generation in Euclidean de Sitter space
• Nonperturbative resummation of de Sitter infrared logarithms in the large-N limit
• Loops in inflationary correlation functions
• Massless interacting quantum fields in deSitter spacetime
• Renormalization group flow and symmetry restoration in de Sitter space
• Photon mass generation during inflation: de Sitter invariant case
• Exact RG Flow in an Expanding Universe and Screening of the Cosmological Constant
• Self Regulation of Infrared Correlations for Massless Scalar Fields during Inflation
• Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths
• Stochastic Effects in Hybrid Inflation
• Solving Stochastic Inflation for Arbitrary Potentials
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• Spontaneous symmetry breaking in inflationary cosmology: on the fate of Goldstone Bosons
• Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: the ladder-rainbow approximation
• Nonperturbative infrared effects for light scalar fields in de Sitter space
• Quantum corrections to scalar field dynamics in a slow-roll space-time
• Renormalization of the 2PI Hartree-Fock approximation on de Sitter background in the broken phase
• Symmetry breaking and the Goldstone theorem in de Sitter space
• Fluctuations along supersymmetric flat directions during Inflation
• Large-Scale Suppression from Stochastic Inflation
• On the fate of coupled flat directions during inflation
• Fluctuation-dissipation and equilibrium for scalar fields in de Sitter

Cited by in corpus (59)

• Correlation Functions in Stochastic Inflation
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Is a Higgs Vacuum Instability Fatal for High-Scale Inflation?
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Stochastic Ultra Slow Roll Inflation
• An effective field theory during inflation II: stochastic dynamics and power spectrum suppression
• De Sitter Diagrammar and the Resummation of Time
• Effective long wavelength scalar dynamics in de Sitter
• Scalar field correlator in de Sitter space at next-to-leading order in a 1/N expansion
• Multiple Fields in Stochastic Inflation
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Stochastic Inflation at NNLO
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Scalar correlation functions in de Sitter space from the stochastic spectral expansion
• On the IR Divergences in de Sitter Space: loops, resummation and the semi-classical wavefunction
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation
• Review on stochastic approach to inflation
• Long distance behavior of $O(N)$-model correlators in de Sitter space and the resummation of secular terms
• Tunneling in Stochastic Inflation
• Functional renormalization group in stochastic inflation
• The quantum Fokker-Planck equation of stochastic inflation
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Large fluctuations and Primordial Black Holes
• Inflationary stochastic anomalies
• Numerical stochastic inflation constrained by frozen noise
• Scalar correlation functions for a double-well potential in de Sitter space
• Stochastic non-attractor inflation
• Thermal Interpretation of Infrared Dynamics in de Sitter
• Swampland conjectures in hybrid metric-Palatini gravity
• Stochastic Effects in Anisotropic Inflation
• Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview
• Fermionic influence (action) on inflationary fluctuations
• Quantum corrections to inflation: the importance of RG-running and choosing the optimal RG-scale
• Boundary Crossing in Stochastic Inflation with Critical Number of Fields
• Unequal time correlators of stochastic scalar fields in de Sitter space
• Light scalars on cosmological backgrounds
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Feynman Rules for Stochastic Inflationary Correlators
• The $1/N$ expansion for stochastic fields in de Sitter spacetime
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Computing First-Passage Times with the Functional Renormalisation Group
• Quantum corrections to inflaton dynamics, the semi-classical approach and the semi-classical limit
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• Free scalar correlators in de Sitter via the stochastic approach beyond slow roll
• Stochastic Baryogenesis
• Inflation with Stochastic Boundary
• Spatial correlations of dark energy from quantum fluctuations in inflation
• Quantitative classicality in cosmological interactions during inflation
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• $\Delta \mathcal{N}$ and the stochastic conveyor belt of Ultra Slow-Roll
• Stochastic Inflation with Interacting Noises
• Time-reversed Stochastic Inflation
• Deviations from Gaussian White Noise in Stochastic Inflation
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Scalar field effective potentials in de Sitter spacetime
• Non-equilibrium evolution of quantum fields during inflation and late accelerating expansion
• A Tail of Eternal Inflation
• Sub-Leading Logarithms for Scalar Potential Models on de Sitter