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
17 - Riemann Tensor Correlator 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 the linearized Riemann tensor correlator on a de Sitter background including one-loop corrections from conformal fields is derived. The Riemann tensor correlation function exhibits interesting features: it is gauge-invariant even when including contributions from loops of matter fields, but excluding graviton loops as it is implemented in the 1/N expansion, it is compatible with de Sitter invariance, and provides a complete characterization of the local geometry. The two-point correlator function of the Riemann tensor is computed by taking suitable derivatives of the metric correlator function found in the previous chapter, and the result is written in a manifestly de Sitter-invariant form. Moreover, given the decomposition of the Riemann tensor in terms of Weyl and Ricci tensors, we write the explicit results for the Weyl and Ricci tensors correlators as well as the Weyl–Ricci tensors correlator and study both their subhorizon and superhorizon behavior. These results are extended to general conformal field theories. We also derive the Riemann tensor correlator in Minkowski spacetime in a manifestly Lorentz-invariant form by carefully taking the flat-space limit of our result in de Sitter.
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- Semiclassical and Stochastic GravityQuantum Field Effects on Curved Spacetime, pp. 519 - 539Publisher: Cambridge University PressPrint publication year: 2020