Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Conventions and notation
- 1 Modeling the early universe
- 2 Blowing up the universe: inflation
- 3 Observing perturbative quantum gravity: fluctuations
- 4 Quantizing gravity: canonical approach
- 5 Quantizing gravity: path integral approach
- 6 Linking gravity, quantum theory, and thermodynamics
- 7 Creating space and time: the no-boundary proposal
- 8 Interpreting the wave function
- 9 Transitioning to different spacetimes
- 10 Going deeper yet: stringy cosmology
- Appendix A Constants of nature and cosmological quantities
- Appendix B Picard{Lefschetz theory and saddle-point approximation
- Appendix C Useful functions
- Appendix D Solutions to exercises
- Appendix E Guide to the bibliography
- Bibliography
- Index
3 - Observing perturbative quantum gravity: fluctuations
Published online by Cambridge University Press: 02 February 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Conventions and notation
- 1 Modeling the early universe
- 2 Blowing up the universe: inflation
- 3 Observing perturbative quantum gravity: fluctuations
- 4 Quantizing gravity: canonical approach
- 5 Quantizing gravity: path integral approach
- 6 Linking gravity, quantum theory, and thermodynamics
- 7 Creating space and time: the no-boundary proposal
- 8 Interpreting the wave function
- 9 Transitioning to different spacetimes
- 10 Going deeper yet: stringy cosmology
- Appendix A Constants of nature and cosmological quantities
- Appendix B Picard{Lefschetz theory and saddle-point approximation
- Appendix C Useful functions
- Appendix D Solutions to exercises
- Appendix E Guide to the bibliography
- Bibliography
- Index
Summary
After an overview of the observed properties of the cosmic microwave background, we turn to attempts at their explanation. First it is shown that classical statistical fluctuations are not suitable for explaining the primordial perturbations inferred from the temperature fluctuations in the CMB. Then it is shown how to quantize inflationary perturbations, after taking care of diffeomorphism invariance. Exact constant-equation-of-state and approximate slow-roll solutions are derived, both for scalar and tensor fluctuations, and shown to potentially be in accord with observations, if the inflationary model is chosen suitably. A brief discussion of the transition from quantum to effectively classical fluctuations is also included. The chapter concludes with a discussion of the open questions related to inflation.
Keywords
observed temperature fluctuations in the CMBclassical statistical fluctuationscosmological perturbation theorygauge transformationsquantization of primordial perturbationsamplitude and spectral index of scalar and tensor perturbationsquantum-to-classical transitioncomparison to observationspuzzles of inflation
Information
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- Chapter
- Information
- Quantum CosmologyAn Introduction, pp. 58 - 101Publisher: Cambridge University PressPrint publication year: 2026
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