Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalized zeta functions

Abstract

For quantum fields on a curved spacetime with an Euclidean section, we derive a general expression for the stress energy tensor two-point function in terms of the effective action. The renormalized two-point function is given in terms of the second variation of the Mellin transform of the trace of the heat kernel for the quantum fields. For systems for which a spectral decomposition of the wave opearator is possible, we give an exact expression for this two-point function. Explicit examples of the variance to the mean ratio ${\Delta }^{\prime }=(<{\rho }^2>-<\rho {>}^2)/(<\rho {>}^2)$ of the vacuum energy density $\rho$ of a massless scalar field are computed for the spatial topologies of $R^d\times S^1$ and $S^3$, with results of ${\Delta }^{\prime }(R^d\times S^1)=(d+1)(d+2)/2$, and ${\Delta }^{\prime }(S^3)=111$ respectively. The large variance signifies the importance of quantum fluctuations and has important implications for the validity of semiclassical gravity theories at sub-Planckian scales. The method presented here can facilitate the calculation of stress-energy fluctuations for quantum fields useful for the analysis of fluctuation effects and critical phenomena in problems ranging from atom optics and mesoscopic physics to early universe and black hole physics.

Uses revtex

Cited by in corpus (46)

• Stochastic Gravity: Theory and Applications
• Stochastic Gravity: Theory and Applications
• Stochastic semiclassical gravity
• Stochastic semiclassical fluctuations in Minkowski spacetime
• Probing a Gravitational Cat State
• Stochastic semiclassical cosmological models
• Stochastic Gravity
• Stochastic Gravity: A Primer with Applications
• On the semiclassical Einstein-Langevin equation
• Non-equilibrium dynamics of a thermal plasma in a gravitational field
• The Effects of Stress Tensor Fluctuations upon Focusing
• Wave Propagation in Stochastic Spacetimes: Localization, Amplification and Particle Creation
• Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space
• Fluctuations of the Hawking Flux
• Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes
• Vacuum Energy Density Fluctuations in Minkowski and Casimir States via Smeared Quantum Fields and Point Separation
• Cosmological perturbations from stochastic gravity
• Spacelike Fluctuations of the Stress Tensor for de Sitter Vacuum
• Direct $\zeta$-function approach and renormalization of one-loop stress tensors in curved spacetimes
• Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric
• Fluctuations of Energy Density and Validity of Semiclassical Gravity
• Fluctuations in the current and energy densities around a magnetic flux carrying cosmic string
• A Kinetic Theory Approach to Quantum Gravity
• Fluctuations of quantum fields via zeta function regularization
• Quantum Fluctuations of Radiation Pressure
• Static black hole solutions with a self interacting conformally coupled scalar field
• Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
• Minkowski Vacuum Stress Tensor Fluctuations
• Quantum Noise of Gravitons and Stochastic Force on Geodesic Separation
• Stochastic Spacetime and Brownian Motion of Test Particles
• Exploring Accelerating Hairy Black Holes in $2+1$ Dimensions: The Asymptotically Locally Anti-de Sitter Class and its Holography
• Noise induced transitions in semiclassical cosmology
• Stress-energy Tensor Correlators of a Quantum Field in Euclidean $R^N$ and $Ad{S}^N$ spaces via the generalized zeta-function method
• zeta-function regularization and one-loop renormalization of field fluctuations in curved space-times
• Horizon entanglement area law from regular black hole thermodynamics
• Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes
• Energy Flux Correlations and Moving Mirrors
• Breakdown of the semiclassical approximation during the early stages of preheating
• Stochastic Gravity: Beyond Semiclassical Gravity
• Quantum Fluctuations of a Coulomb potential
• Noise induced inflation
• Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
• Gravitational spectral shift caused by Casimir stresses
• Correlations of the stress-energy tensor in AdS spaces via the generalized zeta-function method
• Semi-classical wormholes and time machines are unstable
• Aspects and applications of quantum field theory on spaces with conical singularities