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
- Part IV Cosmological and Black Hole Backreaction with Fluctuations
- Part V Quantum Curvature Fluctuations in de Sitter Spacetime
- 15 Stress-Energy Tensor Fluctuations in de Sitter Space
- 16 Two-Point Metric Perturbations in de Sitter
- 17 Riemann Tensor Correlator in de Sitter
- 18 Epilogue: Linkage with Quantum Gravity
- References
- Index
16 - Two-Point Metric Perturbations in de Sitter
from Part V - Quantum Curvature Fluctuations in de Sitter Spacetime
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
- Part IV Cosmological and Black Hole Backreaction with Fluctuations
- Part V Quantum Curvature Fluctuations in de Sitter Spacetime
- 15 Stress-Energy Tensor Fluctuations in de Sitter Space
- 16 Two-Point Metric Perturbations in de Sitter
- 17 Riemann Tensor Correlator in de Sitter
- 18 Epilogue: Linkage with Quantum Gravity
- References
- Index
Summary
In this chapter we derive the full two-point quantum metric perturbations on a de Sitter background including one-loop corrections from conformal fields. We do the calculation using the CTP effective action with the 1/N expansion, and select an asymptotic initial state by a suitable prescription that defines the vacuum of the interacting theory. The decomposition of the metric perturbations into scalar, vector and tensor perturbations is reviewed, and the effective action is given in terms of that decomposition. We first compute the two-point function of the tensor perturbations, which are dynamical degrees of freedom. The relation with the intrinsic and induced fluctuations of stochastic gravity is discussed. We then compute the two-point metric perturbations for the scalar and vector modes, which are constrained degrees of freedom. The result for the full two-point metric perturbations is invariant under spatial rotations and translations as well as under a simultaneous rescaling of the spatial and conformal time coordinates. Finally, our results are extended to general conformal field theories, even strongly interacting ones, by deriving the effective action for a general conformal field theory.
Keywords
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- Information
- Semiclassical and Stochastic GravityQuantum Field Effects on Curved Spacetime, pp. 483 - 518Publisher: Cambridge University PressPrint publication year: 2020