Stochastic Quantum Gravitational Inflation

Abstract

During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinskii's technique of stochastic inflation not only reproduces the leading infrared logarithms at each order in perturbation theory, it can sometimes be summed to reveal what happens when inflation has proceeded so long that the large logarithms overwhelm even very small coupling constants. It is thus a cosmological analogue of what the renormalization group does for the ultraviolet logarithms of quantum field theory, and generalizing this technique to quantum gravity is a problem of great importance. There are two significant differences between gravity and the scalar models for which stochastic formulations have so far been given: derivative interactions and the presence of constrained fields. We use explicit perturbative computations in two simple scalar models to infer a set of rules for stochastically formulating theories with these features.

43 pages, LaTeX 2epsilon, 2 figures (uses epsfig), substantial changes to sections 5 and 8

References in corpus (16)

• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Quantum effects can render w<-1 on cosmological scales
• Super-Acceleration from Massless, Minimally Coupled ${\varphi }^4$
• The Quantum Gravitational Back-Reaction On Inflation
• Quantum Gravity Slows Inflation
• Renormalization Group Theory for Global Asymptotic Analysis
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• One Loop Vaccum Polarization in a Locally de Sitter Background
• One Loop Graviton Self-Energy In A Locally De Sitter Background
• Dynamical renormalization group approach to relaxation in quantum field theory
• No One Loop Back_Reaction In Chaotic Inflation
• Particle decay during inflation: self-decay of inflaton quantum fluctuations during slow roll
• Particle decay in inflationary cosmology
• Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
• Matter Contributions to the Expansion Rate of the Universe
• Out of Equilibrium Fields in Self-consistent Inflationary Dynamics. Density Fluctuations

Cited by in corpus (212)

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• Stochastic Inflationary Scalar Electrodynamics
• Infrared effects in inflationary correlation functions
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Leading Log Solution for Inflationary Yukawa
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• Stochastic growth of quantum fluctuations during slow-roll inflation
• One-loop corrections to the curvature perturbation from inflation
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• The Fermion Self-Energy during Inflation
• On Resumming Inflationary Perturbations beyond One-loop
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• 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
• Classical approximation to quantum cosmological correlations
• Ultra-slow-roll inflation with quantum diffusion
• An effective field theory during inflation: reduced density matrix and its quantum master equation
• Reply to `Can infrared gravitons screen $\Lambda$?'
• Higgs Dynamics during Inflation
• Effective potential for quantum scalar fields on a de Sitter geometry
• Observational Viability and Stability of Nonlocal Cosmology
• Gravitons Enhance Fermions during Inflation
• Is a Higgs Vacuum Instability Fatal for High-Scale Inflation?
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Stochastic inflation beyond slow roll
• Two loop stress-energy tensor for inflationary scalar electrodynamics
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• Nonperturbative resummation of de Sitter infrared logarithms in the large-N limit
• Two Loop Scalar Bilinears for Inflationary SQED
• 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
• Perturbative Quantum Gravity Comes of Age
• The Zeta-Zeta Correlator Is Time Dependent
• Effective long wavelength scalar dynamics in de Sitter
• Multiple Fields in Stochastic Inflation
• Charged Scalar Self-Mass during Inflation
• Scalar field correlator in de Sitter space at next-to-leading order in a 1/N expansion
• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• A parton picture of de Sitter space during slow-roll inflation
• Characters of different secular effects in various patches of de Sitter space
• Renormalization group flow and symmetry restoration in de Sitter space
• A Completely Regular Quantum Stress Tensor with $w<-1$
• Power spectrum in stochastic inflation
• Failure of the stochastic approach to inflation beyond slow-roll
• Scalar Field Equations from Quantum Gravity during Inflation
• Infrared dynamics of the massive ${\varphi }^4$ theory on de Sitter space
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• Gauge-Independent Scales Related to the Standard Model Vacuum Instability
• Inflationary Infrared Divergences: Geometry of the Reheating Surface vs. delta N Formalism
• One Loop Corrected Mode Functions for SQED during Inflation
• IR divergences and kinetic equation in de Sitter space. (Poincare patch; Principal series)
• Minimal decoherence from inflation
• The Graviton Propagator in de Donder Gauge on de Sitter Background
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Infrared resummation for derivative interactions in de Sitter space
• Infrared dynamics of massive scalars from the complementary series in de Sitter space
• Predictions in eternal inflation
• Effective Field Theory out of Equilibrium: Brownian quantum fields
• 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
• Statistical nature of infrared dynamics on de Sitter background
• Excitation of Photons by Inflationary Gravitons
• 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
• Cosmological UV/IR Divergences and de-Sitter Spacetime
• A Simplified Quantum Gravitational Model of Inflation
• Stability of de Sitter spacetime against infrared quantum scalar field fluctuations
• Review on stochastic approach to inflation
• $O(N)$ model in Euclidean de Sitter space: beyond the leading infrared approximation
• Solution of the Dyson--Schwinger equation on de Sitter background in IR limit
• Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
• Backreaction and Stochastic Effects in Single Field Inflation
• Infrared dynamics of a light scalar field in de Sitter
• Non-linear sigma model in de Sitter space
• A Phenomenological Model for the Early Universe
• Dynamical RG and Critical Phenomena in de Sitter Space
• A Gravitational Mechanism for Cosmological Screening
• Hot Accelerated Qubits: Decoherence, Thermalization, Secular Growth and Reliable Late-time Predictions
• Infra-red effects of Non-linear sigma model in de Sitter space
• Issues Concerning Loop Corrections to the Primordial Power Spectra
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• Markovian Dynamics in de Sitter
• Cosmology is not a Renormalization Group Flow
• Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge
• Decoherence in an Interacting Quantum Field Theory: The Vacuum Case
• Quantum corrections to the primordial tensor spectrum: Open EFTs & Markovian decoupling of UV modes
• Physical meaning and consequences of the loop IR divergences in global dS
• Quantum Gravitational Effects on Massive Fermions during Inflation I
• Summing Inflationary Logarithms in Nonlinear Sigma Models
• Backreaction of superhorizon scalar field fluctuations on a de Sitter geometry : a renormalisation group perspective
• Can all the infrared secular growth really be understood as increase of classical statistical variance?
• Long distance behavior of $O(N)$-model correlators in de Sitter space and the resummation of secular terms
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• Tunneling in Stochastic Inflation
• Lagrangian Formulation of Stochastic Inflation: A Recursive Approach
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• Backreaction in Cosmology
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach
• The quantum Fokker-Planck equation of stochastic inflation
• Constructing Infrared Finite Propagators in Inflating Space-time
• Nonlocal Metric Realizations of MOND
• Physical momentum representation of scalar field correlators in de Sitter space
• Soft Gravitons Screen Couplings in de Sitter Space
• Cosmic Purity Lost: Perturbative and Resummed Late-Time Inflationary Decoherence
• Renormalisation of IR divergences and holography in de Sitter
• Hot Cosmic Qubits: Late-Time de Sitter Evolution and Critical Slowing Down
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Inflationary stochastic anomalies
• A Caveat on Building Nonlocal Models of Cosmology
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• Soft Graviton effects on Gauge theories in de Sitter Space
• Scalar correlation functions for a double-well potential in de Sitter space
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• Numerically modeling stochastic inflation in slow-roll and beyond
• Large Deviations in the Early Universe
• Curved space equilibration vs. flat space thermalization (a short review)
• Thermal Interpretation of Infrared Dynamics in de Sitter
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• Post-Inflationary Evolution via Gravitation
• Boltzmann equation in de Sitter space
• Stochastic Effects in Anisotropic Inflation
• Cosmological Trans-Planckian Conjectures are not Effective
• In-in formalism for the entropy of quantum fields in curved spacetimes
• Dynamical Casimir effect and surprises with loop corrections to it
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• Strong restriction on inflationary vacua from the local gauge invariance I: Local gauge invariance and infrared regularity
• Failure of Perturbation Theory Near Horizons: the Rindler Example
• Renormalization group inspired autonomous equations for secular effects in de Sitter space
• Generalizing Starobinskii's Formalism to Yukawa Theory & to Scalar QED
• The Graviton Tail almost Completely Wags the Dog
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• Quantum Effects of Mass on Scalar Field Correlations and Fluctuations during Inflation
• A quantum heating as an alternative of reheating
• Finding origins of CMB anomalies in the inflationary quantum fluctuations
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• Primordial Density Perturbations and Reheating from Gravity
• Topological surprises in de Sitter QFT in two-dimensions
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• Unequal time correlators of stochastic scalar fields in de Sitter space
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• Light scalars on cosmological backgrounds
• Summing Gravitational Effects from Loops of Inflationary Scalars
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• Feynman Rules for Stochastic Inflationary Correlators
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• Stochastic Samples versus Vacuum Expectation Values in Cosmology
• Metric for Rotating object in Infrared Corrected Nonlocal Gravity Model
• Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons
• Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
• Computing First-Passage Times with the Functional Renormalisation Group
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• 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
• The $1/N$ expansion for stochastic fields in de Sitter spacetime
• Gravity, Horizons and Open EFTs
• IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation
• Free scalar correlators in de Sitter via the stochastic approach beyond slow roll
• Stochastic Inflation and Dimensional Reduction
• Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds
• Symmetry breaking in de Sitter: a stochastic effective theory approach
• Hartree approximation in curved spacetimes revisited II: The semiclassical Einstein equations and de Sitter self-consistent solutions
• Unfinished Business in A Nonlinear Sigma Model on de Sitter Background
• Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude
• de Sitter duality and logarithmic decay of dark energy
• Stochastic Baryogenesis
• Possible Enhancement of High Frequency Gravitational Waves
• Inflation with Stochastic Boundary
• An Improved Cosmological Model
• Primordial Gravitational Waves Enhancement
• One loop corrected conformally coupled scalar mode equations during inflation
• Quantum (in)stability of maximally symmetric space-times
• Testing an Ansatz for the Leading Secular Loop Corrections from Quantum Gravity during Inflation
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Stochastic Inflation and Replica Field Theory
• Non-Gaussian statistics of de Sitter spectators: A perturbative derivation of stochastic dynamics
• Geodesic deviation and particle creation in curved spacetimes
• Entropy Generation at the Horizon Diffuses Cosmological Constant in 2D de Sitter Space
• Non-local cosmological models
• Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime
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• Large Inflationary Logarithms in a Nontrivial Nonlinear Sigma Model
• Causality Implies Inflationary Back-Reaction
• Stochastic Inflation with Interacting Noises
• $\Delta \mathcal{N}$ and the stochastic conveyor belt of Ultra Slow-Roll
• From the Fokker-Planck equation to perturbative QFT's results in de Sitter space
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• A (semi)-exact Hamiltonian for the curvature perturbation $\zeta$
• Deviations from Gaussian White Noise in Stochastic Inflation
• Back-reaction in massless de Sitter QFTs: holography, gravitational DBI action and f(R) gravity
• The hand-made tail: Non-perturbative tails from multifield inflation
• Separate universe in multifield inflation: a phase-space approach
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• A Tail of Eternal Inflation
• Massive holographic QFTs in de Sitter
• Sub-Leading Logarithms for Scalar Potential Models on de Sitter
• Quantum corrections to slow-roll inflation: scalar and tensor modes
• Testing Inflationary Cosmology
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators