String Cosmology Modern String Theory Concepts from the Big Bang to Cosmic Structure Edited by Johanna Erdmenger WILEY-VCH Verlag GmbH & Co. KGaA String Cosmology Edited by Johanna Erdmenger Related Titles Dvorak, R. (ed.) Roos, M. Extrasolar Planets Introduction to Cosmology Formation, Detection and Dynamics 2003 2008 ISBN: 978-0-470-84910-1 ISBN: 978-3-527-40671-5 Shore, S. N. Stern, A., Mitton, J. The Tapestry of Modern Pluto and Charon Astrophysics Ice Worlds on the Ragged Edge of the Solar System 2003 2005 ISBN: 978-0-471-16816-4 ISBN: 978-3-527-40556-5 Liddle, A. Stahler, S. W., Palla, F. An Introduction to Modern The Formation of Stars Cosmology 2004 2003 ISBN: 978-3-527-40559-6 ISBN: 978-0-470-84834-0 Foukal, P. V. Solar Astrophysics 2004 ISBN: 978-3-527-40374-5 String Cosmology Modern String Theory Concepts from the Big Bang to Cosmic Structure Edited by Johanna Erdmenger WILEY-VCH Verlag GmbH & Co. KGaA The Editor All books published by Wiley-VCH are carefully produced. Nevertheless, authors, Priv.-Doz. Dr. Johanna Erdmenger editors, and publisher do not warrant the Max-Planck-Institut information contained in these books, für Physik including this book, to be free of errors. Föhringer Ring 6D Readers are advised to keep in mind that 80805 München statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Cover Library of Congress Card No.: applied for Spieszdesign, Neu-Ulm British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Bibliographic information published Portrait of the Editor by the Deutsche Nationalbibliothek Fotostudio Schönberger, The Deutsche Nationalbibliothek lists this München publication in the Deutsche Nationalbib- liografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form by photoprinting, microfilm, or any other means nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Typesetting le-tex publishing services oHG, Leipzig Printing Strauss GmbH, Mörlenbach Binding Litges & Dopf GmbH, Heppenheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN 978-3-527-40862-7 V Contents Preface XI 1 Introduction to Cosmology and String Theory 1 Johanna Erdmenger and Martin Ammon 1.1 Introduction 1 1.2 Foundations of Cosmology 1 1.2.1 Metric and Einstein Equations 2 1.2.2 Energy Content of the Universe 4 1.2.3 Development of the Universe 6 1.3 Inflation 7 1.3.1 Puzzles Within the Big Bang Model 7 1.3.2 The Concept of Inflation 7 1.4 Fluctuations 9 1.4.1 Characterization of Small Fluctuations 9 1.4.2 Power Spectrum 10 1.4.3 Fluctuations and Inflation 11 1.5 Bosonic String Theory 12 1.5.1 Open and Closed Strings 14 1.5.1.1 Closed Strings 15 1.5.1.2 Open Strings 15 1.5.2 Quantization 16 1.5.3 String Perturbation Theory: Interactions and Scattering Amplitudes 17 1.5.4 Bosonic String Theory in Background Fields 19 1.5.5 Chan–Paton Factors 22 1.5.6 Oriented Versus Unoriented Strings 22 1.6 Superstring Theory 23 1.6.1 The RNS Formalism of Superstring Theory 23 1.6.2 Boundary Conditions for Fermions 24 1.6.2.1 Open Strings 24 1.6.2.2 Closed String 25 1.6.3 Type IIA and Type IIB Superstring 26 1.6.4 Type I Superstring 26 VI Contents 1.6.5 Heterotic Superstring 27 1.7 String Dualities and M-Theory 28 1.7.1 Low-Energy Effective Action of Superstring Theory 28 1.7.2 T-Duality 29 1.7.2.1 T-Duality of Closed Strings 30 1.7.2.2 T-Duality of Open Strings 31 1.7.2.3 T-Duality in Superstring Theory 32 1.7.3 S-Duality 32 1.7.4 Web of Dualities and M-Theory 33 1.7.4.1 Type IIA String Theory and M-Theory 34 1.7.4.2 Heterotic E8 ~ E8 String Theory and M-Theory 35 1.8 D-Branes 36 1.8.1 Effective Action of D-Branes 36 1.8.2 D-Branes as Charged BPS Objects 38 1.9 Compactification 38 1.9.1 String Theory on Calabi–Yau Manifolds 39 1.9.1.1 Low-Energy Effective Theory 40 1.9.2 String Theory on Orbifolds 41 1.9.3 String Moduli and Their Stabilization 42 1.10 String Thermodynamics 43 1.11 Gauge–Gravity Duality 44 1.12 Summary 45 References 45 2 String Inflation I: Brane Inflation 47 Marco Zagermann 2.1 Introduction 47 2.1.1 Inflation in String Theory and Moduli Stabilization 49 2.1.2 Brane Inflation Models 50 2.1.3 The Rest of this Chapter 51 2.2 Moduli Stabilization in Type IIB String Theory 52 2.2.1 Type IIB Calabi–Yau Orientifolds and Their Moduli 52 2.2.2 The Tree-Level Effective Action 56 2.2.3 The Volume Modulus 57 2.2.4 de Sitter Uplifting 58 2.3 Warped D3/D3-Brane Inflation (Slow-Roll) 59 2.3.1 The Warped Throat Geometry 61 2.3.2 Towards Slow-Roll Inflation 61 2.3.3 Volume Stabilization 63 2.3.4 The Inflaton Dependence of W64 2.4 D3/D7-Brane Inflation 67 2.4.1 A Compactified Example 70 2.4.2 Moduli Stabilization 71 2.5 DBI Inflation 73 2.5.1 Generalizing the Slow-Roll Conditions 76 Contents VII 2.6 Gravitational Waves and Inflaton Field Range 77 2.6.1 D3-Branes on a Symmetric Torus 79 2.6.2 D3-Branes in a Warped Throat 79 2.6.3 DBI Inflation 80 2.6.4 Wrapped Branes 81 2.6.5 Other Approaches and Related Work 82 2.7 Conclusions 83 References 84 3 String Inflation II: Inflation from Moduli 89 C.P. Burgess 3.1 Introduction 89 3.1.1 Closed-String Moduli as Inflatons 90 3.1.2 A Brief Roadmap 91 3.1.3 Justifying the Approximations 92 3.2 Accelerated Expansion in Supergravity 92 3.2.1 Accelerated Expansion in Higher Dimensions 92 3.2.2 Acceleration in 4D Supergravity 93 3.3 Type IIB Moduli and Their Stabilization 94 3.3.1 Leading-Order Expressions 94 3.3.2 Corrections to the Leading Approximation 95 3.3.2.1 Leading α Corrections 96 3.3.2.2 String-Loop Corrections 96 3.3.2.3 Superpotential Corrections 97 3.3.3 Supersymmetry Breaking Potentials 98 3.4 Inflation from Kähler Moduli 99 3.4.1 Racetrack Inflation 100 3.4.2 Blow-Up Mode Inflation 103 3.4.3 Fiber Inflation 107 3.4.4 K3-Fibration Calabi–Yaus 107 3.4.5 The Scalar Potential 108 3.4.5.1 Kinetic Terms 111 3.4.5.2 Inflationary Slow Roll 111 3.5 What We’ve Learned so far 116 References 118 4 Cosmic Superstrings 121 Robert C. Myers and Mark Wyman 4.1 Introduction 121 4.1.1 Symmetry Breaking and Topological Defects 122 4.1.2 A Brief Review of Cosmic-String Networks 124 4.1.2.1 Small-Scale Structure 126 4.2 Superstring Theory on Cosmological Scales 127 4.2.1 Low String Tensions? 129 4.2.2 Strings After Inflation? 131 4.2.3 Stability of Cosmic Superstrings? 134 VIII Contents 4.2.3.1 Breakage on Space-Filling Branes 134 4.2.3.2 Confinement by Axion Domain Walls 136 4.2.3.3 “Baryon Decay” 136 4.2.3.4 Tachyon Condensation 137 4.2.3.5 An Example: The KKLMMT Model 137 4.2.4 Novel Physics from Cosmic Superstrings 140 4.2.4.1 Potential Problems for Superstring Networks 142 4.3 Observing Cosmic Superstrings 143 4.3.1 Experimental Limits and Observational Tests 144 4.3.1.1 Current Limits 144 4.3.1.2 Signatures Testable by Near-Term Observations 146 4.3.2 Novel Physics from Cosmic Superstrings: Observational Aspects 149 4.3.2.1 Reduced Intercommutation Rates 149 4.3.2.2 Cosmic (p, q)-Strings 150 4.3.3 Monopoles and Beads 150 4.3.4 Semilocal Strings 151 4.3.5 Miscellaneous Observations 151 4.4 Conclusion 152 References 152 5 The CMB as a Possible Probe of String Theory 157 Gary Shiu 5.1 Introduction 157 5.2 String Theory and Inflation 158 5.3 Example 1: Initial State of Inflation 160 5.3.1 Initial State Effects in the CMB and Their Relation to New Physics 163 5.3.2 Corrections to the Primordial Spectrum from Scale-Invariant Initial Conditions 165 5.3.3 Corrections to the Primordial Spectrum from Boundary EFT 165 5.3.4 Observable Parameters and Physical Quantities 167 5.4 Example 2: Non-Gaussianities in the CMB 169 5.4.1 The Shape of Non-Gaussianities and Experimental Constraints 173 5.5 Example 3: Probing the Shape of Extra Dimensions 177 5.5.1 The Warped Deformed Conifold and Other Warped Throats 178 5.5.2 Observing Warped Geometries via the CMB 182 5.6 Summary and Future Directions 186 References 188 6 String Gas Cosmology 193 Robert H. Brandenberger 6.1 Introduction 193 6.1.1 Motivation 193 6.1.2 The Current Paradigm of Early Universe Cosmology 193 Contents IX 6.1.3 Challenges for String Cosmology 195 6.1.4 Preview 197 6.2 Basics of String Gas Cosmology 197 6.2.1 Principles of String Gas Cosmology 197 6.2.2 Dynamics of String Gas Cosmology 199 6.3 Moduli Stabilization in String Gas Cosmology 203 6.3.1 Principles 203 6.3.2 Stabilization of Geometrical Moduli 204 6.3.3 Dilaton Stabilization 207 6.4 String Gas Cosmology and Structure Formation 209 6.4.1 Overview 209 6.4.2 String Thermodynamics 212 6.4.3 Spectrum of Cosmological Fluctuations 217 6.4.4 Spectrum of Gravitational Waves 219 6.4.5 Discussion 221 6.5 Conclusions 222 References 225 7 Gauge–Gravity Duality and String Cosmology 231 Sumit R.