Stochastic semiclassical fluctuations in Minkowski spacetime

Abstract

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a ``non-perturbative'' behavior in some characteristic correlation lengths.

28 pages, RevTeX, no figures

Cited by in corpus (49)

• Stochastic Gravity: Theory and Applications
• Stochastic Gravity: Theory and Applications
• Stochastic description for open quantum systems
• Quantum metric fluctuations and Hawking radiation
• Coarse-Grained Effective Action and Renormalization Group Theory in Semiclassical Gravity and Cosmology
• Stochastic Gravity: A Primer with Applications
• Induced quantum metric fluctuations and the validity of semiclassical gravity
• Stress Tensor Correlators in the Schwinger-Keldysh Formalism
• Can Spacetime be a Condensate?
• One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity
• One-loop gravitational wave spectrum in de Sitter spacetime
• Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space
• Riemann correlator in de Sitter including loop corrections from conformal fields
• Stress tensor fluctuations in de Sitter spacetime
• Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes
• Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
• Cosmological perturbations from stochastic gravity
• Beyond the semi-classical description of black hole evaporation
• Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric
• Scalar Contribution to the Graviton Self-Energy during Inflation
• Vacuum decay in quantum field theory
• A Kinetic Theory Approach to Quantum Gravity
• Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
• Possible Constraints on the Duration of Inflationary Expansion from Quantum Stress Tensor Fluctuations
• Propagation in a thermal graviton background
• Gravitational Decoherence: A Thematic Overview
• Quantum Noise of Gravitons and Stochastic Force on Geodesic Separation
• Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --
• Inflationary Scalars Don't Affect Gravitons at One Loop
• Solving the Effective Field Equations for the Newtonian Potential
• Stress-energy Tensor Correlators of a Quantum Field in Euclidean $R^N$ and $Ad{S}^N$ spaces via the generalized zeta-function method
• Uniformly Accelerated Mirrors. Part 2: Quantum Correlations
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity
• One Loop Field Strengths of Charges and Dipoles on a Locally de Sitter Background
• Chaos, decoherence and quantum cosmology
• Quantum gravitational corrections for spinning particles
• Gravity, Quantum Fields and Quantum Information: Problems with classical channel and stochastic theories
• Master equation for quantum Brownian motion derived by stochastic methods
• Classical Einstein-Langevin Equation and Proposed Applications
• Cosmological bounds on TeV-scale physics and beyond
• Fully renormalized stress tensor correlator in flat space
• Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime
• Stochastic Gravity: Beyond Semiclassical Gravity
• Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime-II
• Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
• Quantum Brownian representation for the quantum field modes
• Testing classical-quantum gravity with geodesic deviation
• The Third Structure Function