Quantum gravity and quantum cosmology
Calcagni, Gianluca & Others Eds.
Quantum gravity and quantum cosmology - New York Springer 2013 - xii,399p. - Lecture Notes in Physics Vol.863 .
Contents
Part I Quantum Gravity
1 String Theory, Unification and Quantum Gravity 3
K.S. Stelle
1.1 Introduction: The Ultraviolet Problems of Gravity 3
1.2 String Theory Basics 5
1.2. l Reparametrization Invariance 6
1.2.2 The String Action 7
1.3 Effective Field Equations 10
1.4 Dimensional Reduction and T-Duality 12
1.4.1 Dimensional Reduction of Strings and T-Duality 13
1.5 M-Theory and the Web of Dualities 15
1.6 Branes and Duality 17
1.7 The Onset of Supergravity Divergences 20
1.7.1 Supergravity Counterterm Analysis 22
1.7.2 Supergravity Divergences from Superstrings 25
1.8 Other Aspects of String Theory 26
1.8.1 The String Scale 26
1.8.2 Boundaries of Moduli Space 27
1.8.3 String and Gravity Thermodynamics 28
1.9 Conclusion 28
References 29
2 Introduction to Loop Quantum Gravity and Cosmology 31
Abhay Ashtekar
2.1 Introduction 31
2.1.1 Development of Quantum Gravity: A Bird's Eye View 31
2.1.2 Physical Questions of Quantum Gravity 36
2.2 Loop Quantum Gravity and Cosmology 38
2.2.1 Viewpoint 38
2.2.2 Advances 40
2.2.3 Challenges and Opportunities 47
References 55
3 Covariant Loop Gravity 57
Carlo Rovelli
3.1 The Definition of the Theory 57
3.2 Properties 58
3.3 The Discretization of Parametrized Systems 59
3.4 The Discretization of Classical General Relativity 62
3.5 Conclusion 64
References 65
4 Spinor Gravity and Diffeomorphism Invariance on the Lattice 67
C. Wetterich
4.1 Introduction 67
4.2 Spinors as Fundamental Degrees of Freedom 68
4.3 Action and Functional Integral 71
4.4 Generalized Lorentz Transformations 72
4.5 Lorentz Invariant Spinar Bilinears 74
4.6 Action with Local Lorentz Symmetry 75
4.7 Gauge and Discrete Symmetries 77
4.8 Discretization 78
4.9 Lattice Action 79
4.10 Lattice Diffeomorphism Invariance 81
4.11 Lattice Diffeomorphism Invariance in Two Dimensions 83
4.12 Effective Action 86
4.13 Metric 87
4.14 Effective Action for Gravity and Gravitational Field Equations 89
4.15 Conclusions and Discussion 90
References 92
5 Introduction to Causal Dynamical Triangulations 93
Andrzej Gorlich
5.1 Introduction 93
5.1.1 Causal Triangulations 94
5.1.2 The Regge Action and the Wick Rotation 96
5.2 Phase Diagram 98
5.3 The Macroscopic de Sitter Universe 100
5.3.1 The Spatial Volume 100
5.3.2 The Mini-superspace Model 102
5.3.3 The Four-Dimensional Space-Time 103
5.4 Quantum Fluctuations 107
5.4.1 The Effective Action 109
5.4.2 Flow of the Gravitational Constant 112
5.5 The Geometry of Spatial Slices 113
5.5.1 The Hausdorff Dimension 113
5.5.2 Spectral Dimension 115
5.6 Conclusions 116
References 116
6 Massive Gravity: A Primer 119
E.A. Bergshoeff, M. Kovacevic, J. Rosseel, and Y. Yin
6.1 Introduction 119
6.2 General Spin 121
6.2.1 "Boosting up the Derivatives" 121
6.2.2 "Taking the Square Root" 125
6.3 Spin 1 126
6.4 Spin 2 131
6.4.1 3D New Massive Gravity 131
6.4.2 3D Topological Massive Gravity 136
6.4.3 Extensions 138
6.5 Conclusions 139
Appendix Exercises 139
References 144
Part II Quantum Cosmology
7 Loop Quantum Cosmology, Space-Time Structure, and Falsifiability 149
Martin Bojowald
7.1 Introduction 149
7.2 Canonical Gravity 153
7.2.1 Cosmic Subtleties 154
7.2.2 Deformations of Space 156
7.2.3 Gauge Theory 157
7.2.4 Quantum Corrections 159
7.3 Loop Quantum Gravity 160
7.3.1 Corrections from Loop Quantum Gravity 162
7.3.2 Construction of Inverse-Triad Corrections 163
7.3.3 Anomaly-Freedom 164
7.3.4 Falsifiability 166
7.3.5 Anomaly-Free Holonomy Corrections 167
7.4 Effective Theories 168
7.4.1 Effective Canonical Dynamics 170
7.4.2 Moment Dynamics 172
7.4.3 Effective Constraints 174
7.4.4 Isotropic Cosmology 177
7.4.5 Beginning 179
7.5 Conclusions 181
References 181
8 Asymptotic Safety, Fractals, and Cosmology 185
Martin Reuter and Frank Saueressig
8.1 Introduction 185
8.2 Theory Space and Its Truncation 188
8.3 The Effective Average Action for Gravity 192
8.4 The Einstein-Hilbert Truncation 194
8.5 The Multi-fractal Properties of QEG Space-Times 197
8.6 Spectral, Walk, and Hausdorff Dimension 200
8.7 Fractal Dimensions Within QEG 202
8. 7 .1 Diffusion Processes on QEG Space-Times 202
8.7.2 The Spectral Dimension in QEG 204
8.7.3 The Walk Dimension in QEG 206
8.7.4 The Hausdorff Dimension in QEG 206
8.7.5 Relations Between Dimensions 207
8.8 The RG Running of Ds and Dw 207
8.9 Matching the Spectral Dimensions of QEG and CDT 210
8.10 Asymptotic Safety in Cosmology 213
8.10.1 RG Improved Einstein Equations 214
8.10.2 Solving the RG Improved Einstein Equations 214
8.10.3 Inflation in the Fixed-Point Regime 215
8.10.4 Entropy and the Renormalization Group 217
8.10.5 Primordial Entropy Generation 219
8.10.6 Entropy Production for RG Trajectory Realized by Nature 221
8.11 Conclusions 223
References 223
9 Holography for Inflationary Cosmology 227
Paul McFadden
9.1 Introduction 227
9.2 Domain-Walls and Cosmologies 230
9.2.1 Defining the Perturbations 230
9.2.2 Dynamics 232
9.2.3 The Domain-Wall/Cosmology Correspondence 234
9.2.4 Cosmological Power Spectra 236
9.3 Holography for Cosmology 237
9.3.1 Background Solutions 238
9.3.2 Basics of Holography 238
9.3.3 Hamiltonian Holographic Renormalisation 240
9.3.4 The Stress Tensor 2-Point Function 243
9.3.5 Holographic Analysis 244
9.3.6 Holographic Formulae for the Power Spectra 249
9.4 Holographic Phenomenology for Cosmology 250
9.4.1 A Prototype Dual QFT 251
9.4.2 Calculating the Holographic Power Spectra 252
9.5 Confronting Observations 257
9.6 Conclusion 263
References 265
Part III Observational Status
10 Observational Status of Dark Matter 271
Joseph Silk
10.1 Introduction 271
10.2 The Observational Case 272
10.3 From Galaxies to Clusters 272
10.3.1 Galaxy Rotation Curves 272
10.4 Large-Scale Structure 274
10.4.1 Redshift Space Distortions 274
10.4.2 Baryon Acoustic Oscillations 275
10.4.3 Cosmic Microwave Background 275
10.5 Future Prospects in Observation 275
10.6 Future Prospects in Astrophysical Theory 276
10.7 Direct Detection 279
10.8 Indirect Detection 279
10.8.1 Helioseismology 280
10.8.2 High Energy Cosmic Rays 280
10.8.3 Gamma Rays 281
10.8.4 The WMAP Microwave Haze 281
10.8.5 Decaying Dark Matter 282
10.9 The Future 282
10.9.1 The Sun 282
10.9.2 Direct Detection 283
10.9.3 Air Cerenkov Telescopes 283
10.9.4 Strange Stars 283
10.9.5 The Galactic Centre 284
10.9.6 LHC 284
10.10 Summary 284
References 285
11 Dark Energy: Observational Status and Theoretical Models 289
Shinji Tsujikawa
11.1 Introduction 289
11.2 Observational Constraints on Dark Energy 291
11.2.1 Supernov~ Ia Observations 291
11 .2.2 CMB 294
11.2.3 BAO 296
11.3 Cosmological Constant . 298
11.4 Modified Matter Models 300
11.4.1 Quintessence 301
11.4.2 k-Essence 304
11.4.3 Coupled Dark Energy 307
11.4.4 Unified Models of Dark Energy and Dark Matter 311
11.5 Modified Gravity Models 313
11.5 .1 f (R) Gravity 313
11.5.2 Scalar-Tensor Theories 319
11.5.3 DGPModel 323
11.6 Conclusions 325
References 326
12 Unconventional Cosmology 333
Robert H. Brandenberger
12.1 Introduction 333
12.1.1 Overview 333
12.1.2 Review oflnflationary Cosmology 335
12.1.3 Conceptual Problems oflnflationary Cosmology 337
12.2 Matter Bounce 339
12.2.1 The Idea 339
12.2.2 Realizing a Matter Bounce with Modified Matter 342
12.2.3 Realizing a Matter Bounce with Modified Gravity 344
12.3 Emergent Universe 345
12.3.1 The Idea 345
12.3.2 String Gas Cosmology 347
12.4 Cosmological Perturbations 351
12.4.1 Overview 351
12.5 Fluctuations in Inflationary Cosmology 355
12.6 Matter Bounce and Structure Formation 356
12.6.1 Basics 357
12.6.2 Specific Predictions 359
12.7 String Gas Cosmology and Structure Formation 361
12.7.1 Overview 361
12.7.2 Spectrum of Cosmological Fluctuations 363
12.7.3 Key Prediction of String Gas Cosmology 365
12.7.4 Comments 367
12.8 Conclusions 367
References 368
13 Quantum Gravity and Inflation 375
M.G. Romania, N.C. Tsamis, and R.P. Woodard
13.1 Introduction 375
13.2 Model Building 381
13.3 Post-Inflationary Evolution 391
13.4 Conclusions 393
References 394
Index 397
9783642330353
Irrigation
Quantum cosmology
Astronomy
Stone
Building materials
530.143 / CAL
Quantum gravity and quantum cosmology - New York Springer 2013 - xii,399p. - Lecture Notes in Physics Vol.863 .
Contents
Part I Quantum Gravity
1 String Theory, Unification and Quantum Gravity 3
K.S. Stelle
1.1 Introduction: The Ultraviolet Problems of Gravity 3
1.2 String Theory Basics 5
1.2. l Reparametrization Invariance 6
1.2.2 The String Action 7
1.3 Effective Field Equations 10
1.4 Dimensional Reduction and T-Duality 12
1.4.1 Dimensional Reduction of Strings and T-Duality 13
1.5 M-Theory and the Web of Dualities 15
1.6 Branes and Duality 17
1.7 The Onset of Supergravity Divergences 20
1.7.1 Supergravity Counterterm Analysis 22
1.7.2 Supergravity Divergences from Superstrings 25
1.8 Other Aspects of String Theory 26
1.8.1 The String Scale 26
1.8.2 Boundaries of Moduli Space 27
1.8.3 String and Gravity Thermodynamics 28
1.9 Conclusion 28
References 29
2 Introduction to Loop Quantum Gravity and Cosmology 31
Abhay Ashtekar
2.1 Introduction 31
2.1.1 Development of Quantum Gravity: A Bird's Eye View 31
2.1.2 Physical Questions of Quantum Gravity 36
2.2 Loop Quantum Gravity and Cosmology 38
2.2.1 Viewpoint 38
2.2.2 Advances 40
2.2.3 Challenges and Opportunities 47
References 55
3 Covariant Loop Gravity 57
Carlo Rovelli
3.1 The Definition of the Theory 57
3.2 Properties 58
3.3 The Discretization of Parametrized Systems 59
3.4 The Discretization of Classical General Relativity 62
3.5 Conclusion 64
References 65
4 Spinor Gravity and Diffeomorphism Invariance on the Lattice 67
C. Wetterich
4.1 Introduction 67
4.2 Spinors as Fundamental Degrees of Freedom 68
4.3 Action and Functional Integral 71
4.4 Generalized Lorentz Transformations 72
4.5 Lorentz Invariant Spinar Bilinears 74
4.6 Action with Local Lorentz Symmetry 75
4.7 Gauge and Discrete Symmetries 77
4.8 Discretization 78
4.9 Lattice Action 79
4.10 Lattice Diffeomorphism Invariance 81
4.11 Lattice Diffeomorphism Invariance in Two Dimensions 83
4.12 Effective Action 86
4.13 Metric 87
4.14 Effective Action for Gravity and Gravitational Field Equations 89
4.15 Conclusions and Discussion 90
References 92
5 Introduction to Causal Dynamical Triangulations 93
Andrzej Gorlich
5.1 Introduction 93
5.1.1 Causal Triangulations 94
5.1.2 The Regge Action and the Wick Rotation 96
5.2 Phase Diagram 98
5.3 The Macroscopic de Sitter Universe 100
5.3.1 The Spatial Volume 100
5.3.2 The Mini-superspace Model 102
5.3.3 The Four-Dimensional Space-Time 103
5.4 Quantum Fluctuations 107
5.4.1 The Effective Action 109
5.4.2 Flow of the Gravitational Constant 112
5.5 The Geometry of Spatial Slices 113
5.5.1 The Hausdorff Dimension 113
5.5.2 Spectral Dimension 115
5.6 Conclusions 116
References 116
6 Massive Gravity: A Primer 119
E.A. Bergshoeff, M. Kovacevic, J. Rosseel, and Y. Yin
6.1 Introduction 119
6.2 General Spin 121
6.2.1 "Boosting up the Derivatives" 121
6.2.2 "Taking the Square Root" 125
6.3 Spin 1 126
6.4 Spin 2 131
6.4.1 3D New Massive Gravity 131
6.4.2 3D Topological Massive Gravity 136
6.4.3 Extensions 138
6.5 Conclusions 139
Appendix Exercises 139
References 144
Part II Quantum Cosmology
7 Loop Quantum Cosmology, Space-Time Structure, and Falsifiability 149
Martin Bojowald
7.1 Introduction 149
7.2 Canonical Gravity 153
7.2.1 Cosmic Subtleties 154
7.2.2 Deformations of Space 156
7.2.3 Gauge Theory 157
7.2.4 Quantum Corrections 159
7.3 Loop Quantum Gravity 160
7.3.1 Corrections from Loop Quantum Gravity 162
7.3.2 Construction of Inverse-Triad Corrections 163
7.3.3 Anomaly-Freedom 164
7.3.4 Falsifiability 166
7.3.5 Anomaly-Free Holonomy Corrections 167
7.4 Effective Theories 168
7.4.1 Effective Canonical Dynamics 170
7.4.2 Moment Dynamics 172
7.4.3 Effective Constraints 174
7.4.4 Isotropic Cosmology 177
7.4.5 Beginning 179
7.5 Conclusions 181
References 181
8 Asymptotic Safety, Fractals, and Cosmology 185
Martin Reuter and Frank Saueressig
8.1 Introduction 185
8.2 Theory Space and Its Truncation 188
8.3 The Effective Average Action for Gravity 192
8.4 The Einstein-Hilbert Truncation 194
8.5 The Multi-fractal Properties of QEG Space-Times 197
8.6 Spectral, Walk, and Hausdorff Dimension 200
8.7 Fractal Dimensions Within QEG 202
8. 7 .1 Diffusion Processes on QEG Space-Times 202
8.7.2 The Spectral Dimension in QEG 204
8.7.3 The Walk Dimension in QEG 206
8.7.4 The Hausdorff Dimension in QEG 206
8.7.5 Relations Between Dimensions 207
8.8 The RG Running of Ds and Dw 207
8.9 Matching the Spectral Dimensions of QEG and CDT 210
8.10 Asymptotic Safety in Cosmology 213
8.10.1 RG Improved Einstein Equations 214
8.10.2 Solving the RG Improved Einstein Equations 214
8.10.3 Inflation in the Fixed-Point Regime 215
8.10.4 Entropy and the Renormalization Group 217
8.10.5 Primordial Entropy Generation 219
8.10.6 Entropy Production for RG Trajectory Realized by Nature 221
8.11 Conclusions 223
References 223
9 Holography for Inflationary Cosmology 227
Paul McFadden
9.1 Introduction 227
9.2 Domain-Walls and Cosmologies 230
9.2.1 Defining the Perturbations 230
9.2.2 Dynamics 232
9.2.3 The Domain-Wall/Cosmology Correspondence 234
9.2.4 Cosmological Power Spectra 236
9.3 Holography for Cosmology 237
9.3.1 Background Solutions 238
9.3.2 Basics of Holography 238
9.3.3 Hamiltonian Holographic Renormalisation 240
9.3.4 The Stress Tensor 2-Point Function 243
9.3.5 Holographic Analysis 244
9.3.6 Holographic Formulae for the Power Spectra 249
9.4 Holographic Phenomenology for Cosmology 250
9.4.1 A Prototype Dual QFT 251
9.4.2 Calculating the Holographic Power Spectra 252
9.5 Confronting Observations 257
9.6 Conclusion 263
References 265
Part III Observational Status
10 Observational Status of Dark Matter 271
Joseph Silk
10.1 Introduction 271
10.2 The Observational Case 272
10.3 From Galaxies to Clusters 272
10.3.1 Galaxy Rotation Curves 272
10.4 Large-Scale Structure 274
10.4.1 Redshift Space Distortions 274
10.4.2 Baryon Acoustic Oscillations 275
10.4.3 Cosmic Microwave Background 275
10.5 Future Prospects in Observation 275
10.6 Future Prospects in Astrophysical Theory 276
10.7 Direct Detection 279
10.8 Indirect Detection 279
10.8.1 Helioseismology 280
10.8.2 High Energy Cosmic Rays 280
10.8.3 Gamma Rays 281
10.8.4 The WMAP Microwave Haze 281
10.8.5 Decaying Dark Matter 282
10.9 The Future 282
10.9.1 The Sun 282
10.9.2 Direct Detection 283
10.9.3 Air Cerenkov Telescopes 283
10.9.4 Strange Stars 283
10.9.5 The Galactic Centre 284
10.9.6 LHC 284
10.10 Summary 284
References 285
11 Dark Energy: Observational Status and Theoretical Models 289
Shinji Tsujikawa
11.1 Introduction 289
11.2 Observational Constraints on Dark Energy 291
11.2.1 Supernov~ Ia Observations 291
11 .2.2 CMB 294
11.2.3 BAO 296
11.3 Cosmological Constant . 298
11.4 Modified Matter Models 300
11.4.1 Quintessence 301
11.4.2 k-Essence 304
11.4.3 Coupled Dark Energy 307
11.4.4 Unified Models of Dark Energy and Dark Matter 311
11.5 Modified Gravity Models 313
11.5 .1 f (R) Gravity 313
11.5.2 Scalar-Tensor Theories 319
11.5.3 DGPModel 323
11.6 Conclusions 325
References 326
12 Unconventional Cosmology 333
Robert H. Brandenberger
12.1 Introduction 333
12.1.1 Overview 333
12.1.2 Review oflnflationary Cosmology 335
12.1.3 Conceptual Problems oflnflationary Cosmology 337
12.2 Matter Bounce 339
12.2.1 The Idea 339
12.2.2 Realizing a Matter Bounce with Modified Matter 342
12.2.3 Realizing a Matter Bounce with Modified Gravity 344
12.3 Emergent Universe 345
12.3.1 The Idea 345
12.3.2 String Gas Cosmology 347
12.4 Cosmological Perturbations 351
12.4.1 Overview 351
12.5 Fluctuations in Inflationary Cosmology 355
12.6 Matter Bounce and Structure Formation 356
12.6.1 Basics 357
12.6.2 Specific Predictions 359
12.7 String Gas Cosmology and Structure Formation 361
12.7.1 Overview 361
12.7.2 Spectrum of Cosmological Fluctuations 363
12.7.3 Key Prediction of String Gas Cosmology 365
12.7.4 Comments 367
12.8 Conclusions 367
References 368
13 Quantum Gravity and Inflation 375
M.G. Romania, N.C. Tsamis, and R.P. Woodard
13.1 Introduction 375
13.2 Model Building 381
13.3 Post-Inflationary Evolution 391
13.4 Conclusions 393
References 394
Index 397
9783642330353
Irrigation
Quantum cosmology
Astronomy
Stone
Building materials
530.143 / CAL