Dark Energy: From EFTs to Supergravity

Description

This book addresses supergravity and supergravity-motivated effective field theories in the context of cosmological model building. Extracting information about quintessence from string theory has attracted much attention in the past few years.  The question became more urgent very recently after the possibility of obtaining de Sitter space was called into question. Therefore, there is an interesting debate as to whether de Sitter space or, even, quintessence can be derived from a fundamental theory, string theory or otherwise. This is a very active field of research, and the topics covered in the book render this work very timely. Throughout the book, special care has been taken in demonstrating historical relevance of the field and describing the set of open questions motivating the state-of-the-art research. The first few chapters in each part provide a detailed review of standard perturbative and non-perturbative techniques in supergravity model building, as a way to prepare the reader for the more technical and original subsequent chapters. These early chapters also represent a self-contained review that would be useful for anyone planning to enter this challenging area of study. The subsequent chapters detail research in supergravity-motivated effective field theories, in the first part, and supergravity models, in the second part.   One of the important conclusions in this book is that modelling quintessence in perturbative string theory is at least as challenging as modelling de Sitter, placing the wider programme on a collision course with observations. Supervisor’s Foreword Abstract Publications Related to This Thesis Acknowledgements Contents 1 Introduction and Motivations 1.1 Outline 1.2 Further Resources 1.3 Units and Conventions References Part I String Inspired EFTs 2 Perturbative Supergravity in Type IIB Theories 2.1 Special Geometry of Kähler Manifolds 2.1.1 The Kähler Structure of mathcalMks 2.1.2 The Complex Structure of mathcalMcs 2.2 Perturbative mathcalN=2 Supergravity 2.3 Orientifolding the Supergravity Action 2.3.1 Truncating the Kähler Geometry 2.3.2 The Effective mathcalN=1 Action 2.4 Flux Compactifications 2.5 The Swampland Programme 2.5.1 The Swampland Distance Conjecture 2.5.2 The Refined de Sitter Conjecture References 3 Some Open Questions in Modern Cosmology 3.1 The Hierarchy Problem and Naturalness 3.2 The Cosmological Constant Problem 3.2.1 The Anthropic Principle 3.2.2 Sequestering the Vacuum Energy 3.2.3 Supersymmetry 3.2.4 The Flux Landscape 3.3 Coincidence Problem 3.3.1 Anthropic Considerations 3.3.2 K-Essence Scenarios References 4 A Naturally Light Dark Energy Model 4.1 Clockwork Mechanism 4.2 Dvali-Kaloper-Sorbo Four-Form Model 4.3 Obtaining a Naturally Light Dark Energy Scale 4.4 Warm-Up: A String Motivated Toy Model 4.5 A More In-Depth Look into Achieving the Embedding 4.6 Deconstructing Clockwork Dark Energy 4.7 Conclusions References 5 A Stringy Perspective on the Coincidence Problem 5.1 Generic Idea 5.2 A Toy Model 5.3 Further Discussion References 6 Intermezzo: Supergravity and the Swampland 6.1 A Simple Example of the Backreaction on Moduli Space 6.2 Calculations at the Boundary of Moduli Space 6.2.1 The Type IIB Runaway 6.2.2 The Type IIA Runaway 6.2.3 The Heterotic Runaway 6.3 Divergence of String Diagrams and Perturbative Control or Lack Thereof 6.3.1 Perturbative and Non-perturbative Contributions Spoiling the Vacuum References Part II String Models 7 Corrections to the Supergravity Action in Type IIB 7.1 Review of Type IIB Effective Field Theory 7.2 Non-renormalisation Theorems 7.3 α'3 Corrections 7.4 One-Loop Corrections 7.5 Higher Derivative Corrections 7.6 Non-perturbative Corrections 7.7 Validity of the Effective Description 7.8 KKLT Model Building 7.9 Racetrack Model Building 7.10 LVS Model Building References 8 Obstructions to Quintessence Model Building 8.1 Old Challenges for Quintessence in String Theory 8.1.1 Fifth Forces and Radiative Instability 8.2 The KL Problem for Quintessence 8.2.1 Review of the KL Problem 8.2.2 Racetrack Solution to the KL Problem 8.2.3 General Implications for Quintessence 8.2.4 A Closer Look at Quintessence Models with a KL Problem 8.3 Axion Hilltop Quintessence and Initial Conditions 8.3.1 LVS Axion Hilltop Quintessence 8.3.2 Constraining Hilltops 8.3.3 Stochastic Effects and Initial Conditions 8.4 Discussion References 9 Gauss-Bonnet Curvature Corrections and the Absence of de Sitter Vacua 9.1 Review of Flux Compactifications of the Heterotic String Action and Stability Conditions 9.2 Extending the Montero-van Riet-Venken Bound in the Small Gauss-Bonnet Coupling Limit 9.3 Non-perturbative Conditions for the Existence of de Sitter Solutions with a Gauss-Bonnet Term 9.3.1 Internal Flux 9.3.2 External Flux 9.4 Discussion References 10 Conclusions and Outlooks References Appendix A Details and Calculations for Type IIB Supergravity A.1 Calculations for the Dimensional Reduction of the script upper N equals 2mathcalN=2 Type IIB Action A.1.1 The Dimensional Reduction of the NSNS Sector A.1.2 The Dimensional Reduction of the RR Sector A.2 Dualising the upper C 2C2 and upper B 2B2 Axions Appendix B Type IIA Perturbative Supergravity B.1 script upper N equals 2mathcalN=2 Supergravity Action B.1.1 The RR Sector and the Topological Term of the Type IIA Action B.1.2 Dualising the upper B 2B2 and upper C 3C3 Fields B.2 Orientifolding and script upper N equals 1mathcalN=1 Type IIA Supergravity B.2.1 The Kähler Structure of script upper M overTilde Superscript k stildemathcalMks B.2.2 The Quaternionic Structure of script upper M overTilde Superscript upper QtildemathcalMQ B.3 The Type IIA script upper N equals 1mathcalN=1 Effective Action B.4 Type IIA Flux Compactifications B.5 Moduli Stabilisation in Type IIA Flux Supergravity References