Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background

Abstract

Behaviour of a weekly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). Existence of the de Sitter invariant equilibrium quantum state of the scalar field in the presence of interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculation of an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in the equilibrium state, correlation time and spatial physical correlation radius are presented. The latter does not depend on time that implies that the characteristic size of domains with positive and negative values of the scalar field remains the same on average in the equilibrium state in spite of the expansion of the $t=const$ hypersurface of the de Sitter space-time.

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• Topological Inflation
• Monopoles as Big as a Universe
• Non-Equilibrium Quantum Fields in the Large N Expansion
• Topological Defects as Seeds for Eternal Inflation

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• Initial states and infrared physics in locally de Sitter spacetime
• Non-Gaussianities and Primordial Black Holes
• Cosmological Infrared Subtractions & Infrared-Safe Computables
• Quantum Cosmology in Four Dimensions
• Clocking the End of Cosmic Inflation
• Loop corrections to primordial non-Gaussianity
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Photon propagator for inflation in the general covariant gauge
• Higgs-like spectator field as the origin of structure
• Primordial non-Gaussianity from the Effects of the Standard Model Higgs during Reheating after Inflation
• Big Steve and the State of the Universe
• Relaxation of vacuum energy in q-theory
• Complementarity between Cosmic String Gravitational Waves and long-lived particle searches in a laboratory
• Green's function of the Vector fields on DeSitter Background
• Boundary choices and one-loop complex gravitational path integral
• Is cosmological constant screened in Liouville gravity with matter?
• Scale dependences of local form non-Gaussianity parameters from a DBI isocurvature field
• Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Dark matter cooling during early matter-domination boosts sub-earth halos
• Cosmological Signatures of Neutrino Seesaw Mechanism
• Quantifying the 'naturalness' of the curvaton model
• Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion
• Nonlocality of quantum matter corrections and cosmological constant running
• In-in formalism, pseudo-instantons and rethinking quantum cosmology
• Quantum backreaction of $O(N)$-symmetric scalar fields and de Sitter spacetimes at the renormalization point: renormalization schemes and the screening of the cosmological constant
• Causality Implies Inflationary Back-Reaction
• Inflationary Potentials from the Exact Renormalisation Group
• Large Inflationary Logarithms in a Nontrivial Nonlinear Sigma Model
• Coleman-Weinberg dynamics of ultralight scalar dark matter and GeV-scale right-handed neutrinos
• Functional Renormalisation Group for Brownian Motion I: The Effective Equations of Motion
• Thermal Inflation with a Thermal Waterfall Scalar Field Coupled to a Light Spectator Scalar Field
• Remote Hawking-Moss instanton and the Lorentzian path integral
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Cosmological Non-Gaussianity from Neutrino Seesaw Mechanism
• Gravitational Wave Spectral Shapes as a probe of Long Lived Right-handed Neutrinos, Leptogenesis and Dark Matter: Global versus Local B-L Cosmic Strings
• Cascade Relaxation of the Gravitating Vacuum as a Generator of the Evolving Universe
• Post-Inflationary Dynamics
• Stabilization of Starobinsky-Vilenkin stochastic inflation by an environmental noise
• Magnetogenesis From Baryon Asymmetry During an Early Matter Dominated Era
• Gauss-Bonnet-induced symmetry breaking/restoration during inflation
• Topology of Cosmological Black Holes
• Dark energy without fine tuning
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Higgs domain walls in the thermal background
• From the Fokker-Planck equation to perturbative QFT's results in de Sitter space
• Unravelling Cosmological Perturbations
• Stochastic Inflation with Interacting Noises
• Early universe dynamics of PQ field with very small self-coupling and its implications for axion dark matter
• Probability Density Functionals in Perturbation Theory within the QFT in-in Formalism
• 50 years in the Landau Institute environment
• Slow-roll versus stochastic slow-roll inflation
• Primordial Black Holes in non-linear perturbation theory
• Can Stochastic Clocks in FLRW Minisuperspace Prevent Dynamical Singularities?
• Time-reversed Stochastic Inflation
• Ultralight Dark Matter from the Edge of Field Space
• Deviations from Gaussian White Noise in Stochastic Inflation
• Back-reaction in massless de Sitter QFTs: holography, gravitational DBI action and f(R) gravity
• Warm Inflation Beyond the Markovian Limit
• Hidden in the background: a local approach to CMB anomalies
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• The hand-made tail: Non-perturbative tails from multifield inflation
• Inflationary gravitational wave background as a tail effect
• Inflation: a quantum laboratory on cosmological scales
• Non-linear effects in early Universe cosmology
• Dilaton, Screening of the Cosmological Constant and IR-Driven Inflation
• A (semi)-exact Hamiltonian for the curvature perturbation $\zeta$
• Inflationary quantum dynamics and backreaction using a classical-quantum correspondence
• Probing baryogenesis with gravitational waves
• The Black Hole Window on Cosmic Inflation
• Fingerprints of freeze-in dark matter in an early matter-dominated era
• Semi-classical Einstein equations:descend to the ground state
• Kination cosmology from scalar fields and gravitational-wave signatures
• Separate universe in multifield inflation: a phase-space approach
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Quantum corrections to slow-roll inflation: scalar and tensor modes
• Testing Inflationary Cosmology
• Massive holographic QFTs in de Sitter
• Mori-Zwanzig formalism for early cosmic inflation
• Holographic beta function in de Sitter space
• Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators
• A cross-epoch endpoint-consistency test of a single effective scaling from dark energy to inflation
• A Tail of Eternal Inflation
• Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta N$ formalism
• Correlation length of the angular mode for an approximate $U(1)$ symmetry during inflation
• Sub-Leading Logarithms for Scalar Potential Models on de Sitter
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• On gravitational preheating
• Scalar field effective potentials in de Sitter spacetime
• Stochastic Inflation in Compact Extra Dimensions
• Stochastic isocurvature constraints for axion dark matter with high-scale inflation