Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Overview: Main Themes. Key Issues. Reader’s Guide
- Part I Effective Action and Regularization, Stress Tensor and Fluctuations
- Part II Infrared Behavior, 2PI, I/N, Backreaction and Semiclassical Gravity
- Part III Stochastic Gravity
- 9 Metric Correlations at One-Loop: In-In and Large N
- 10 The Einstein–Langevin Equation
- 11 Metric Fluctuations in Minkowski Spacetime
- Part IV Cosmological and Black Hole Backreaction with Fluctuations
- Part V Quantum Curvature Fluctuations in de Sitter Spacetime
- References
- Index
11 - Metric Fluctuations in Minkowski Spacetime
from Part III - Stochastic Gravity
Published online by Cambridge University Press: 20 January 2020
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Overview: Main Themes. Key Issues. Reader’s Guide
- Part I Effective Action and Regularization, Stress Tensor and Fluctuations
- Part II Infrared Behavior, 2PI, I/N, Backreaction and Semiclassical Gravity
- Part III Stochastic Gravity
- 9 Metric Correlations at One-Loop: In-In and Large N
- 10 The Einstein–Langevin Equation
- 11 Metric Fluctuations in Minkowski Spacetime
- Part IV Cosmological and Black Hole Backreaction with Fluctuations
- Part V Quantum Curvature Fluctuations in de Sitter Spacetime
- References
- Index
Summary
In this chapter we describe an important application of stochastic gravity: we derive the Einstein–Langevin equation for the metric perturbations in a Minkowski background. We solve this equation for the linearized Einstein tensor and compute the associated two-point correlation functions, as well as the two-point correlation functions for the metric perturbations. The results of this calculation show that gravitational fluctuations are negligible at length scales larger than the Planck length and predict that the fluctuations are strongly suppressed at small scales. These results also reveal an important connection between stochastic gravity and the 1/N expansion of quantum gravity. In addition, they are used to study the stability of the Minkowski metric as a solution of semiclassical gravity, which constitutes an application of the validity criterion introduced in the previous chapter. This calculation requires a discussion of the problems posed by the so-called runaway solutions and some of the methods of dealing with them.
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- Semiclassical and Stochastic GravityQuantum Field Effects on Curved Spacetime, pp. 364 - 388Publisher: Cambridge University PressPrint publication year: 2020