Cosmology and String Theory (eBook)

Horatiu Nastase has a career which has spanned 4 continents. He holds a PhD from SUNY Stony Brook in string theory. During a postdoc at the Institute for Advanced Study in Princeton, his work with Berenstein and Maldacena started the pp wave correspondence. After another postdoc and Brown University, and a tenure-track at Tokyo Tech in Japan, he is now a tenured Researcher at IFT-UNESP in Brazil.  

Preface 7
Acknowledgements 8
Contents 9
Introduction 16
Part I Standard Cosmology 18
1 The Expanding Universe and the Big Bang 19
1.1 Observations 19
1.2 Newtonian Approximation for the Expansion of Space 21
1.3 Time Evolution of the Scale Factor for a Linear Equation of State 24
1.4 Universe with Several Matter Components 26
1.5 A Quick History of Experimental Observations and Discoveries 27
1.6 The Cosmological Constant 28
2 Relativistic Theory 31
2.1 The FLRW Metric and the Friedmann Equation 31
2.2 Types of Matter and Resulting Expansion of the Universe 35
2.3 Cosmological Evolution Formulas 37
3 The Propagation of Light and Measurements of Distance, Luminosity and Mass 42
3.1 Propagation of Light 42
3.2 Measurements of Distance by Light 44
3.3 Optical Measurements 45
3.4 Stellar Evolution 48
3.5 Measurements of Distance 49
3.6 Mass Determination for Distant Bodies 52
4 Evidence for Dark Matter and the ?CDM Model 55
4.1 Evidences for Dark Matter 55
4.2 Candidates for Dark Matter 60
4.3 WIMP Dark Matter Candidates 62
4.4 The ?CDM Model 64
5 The Early Universe and Its Thermal History 66
5.1 Defining the Hot Big Bang 66
5.2 Equilibrium Thermodynamics 68
5.3 Thermodynamics of the Universe 71
5.4 Particle Species in the Radiation Dominated (R.D). Era 74
5.5 Neutrino Decoupling 76
6 Big Bang Nucleosynthesis and Recombination 80
6.1 Recombination Temperature 80
6.2 Big Bang Nucleosynthesis 82
6.3 Dependence of BBN Primordial Abundances on Parameters 85
6.4 Observations and Comparison with BBN 86
6.5 Summary of the Thermal History 87
7 The Cosmic Microwave Background Radiation (CMBR) Anisotropy 90
7.1 The CMBR and Its Anisotropy 90
7.2 Kinematics of the CMBR 92
7.3 Perturbation Theory for CMBR 96
7.4 Effect of Density Perturbations on the CMBR 102
8 Problems to Be Solved by Inflation and How They Are Solved in Inflationary Models 107
8.1 Problems with Standard Cosmology Before Inflation 107
8.2 The Paradigm of Inflation 111
8.3 Inflationary Solutions to Cosmological Problems 113
8.4 Inflation with a Scalar Field 118
9 Slow-Roll Inflation 122
9.1 Slow-Roll Analysis 123
9.2 General (Non-slow Roll) Formulas 126
9.3 Slow Roll Conditions 128
9.4 Exact Solution for Inflation 129
9.5 Variants of Inflation 130
9.5.1 Initial Conditions for Inflation 132
10 Reheating and Baryogenesis 134
10.1 Standard Reheating 134
10.2 New Reheating and Preheating 138
10.3 Entropy Production and the Number of e-Folds 140
10.4 Baryogenesis 141
10.5 Relics 142
11 Fluctuations in Inflation and Matching with Experimental Data 144
11.1 Scales During Inflation 144
11.2 Scalar Fluctuations During Inflation 145
11.3 Quantization of Scalar Perturbations 147
11.4 Scalar-Gravity Fluctuations 149
11.5 Power Spectrum and Contact with Experimental Data 152
11.6 Primordial Tensor Perturbations 154
11.7 Constraints on Inflationary Models 156
Part II Elements of String Theory 159
12 Extra Dimensions and Kaluza–Klein 160
12.1 KK Metrics 161
12.2 Fields with Spin 163
12.3 The Original Kaluza–Klein Theory 165
12.4 Generalization: The n-Torus Tn=(S1)timesn 165
13 Electromagnetism and Gravity in Various Dimensions. Consistent Truncations 168
13.1 Review of Electromagnetism and Gravity 168
13.2 Interlude: Spheres in Higher Dimensions 169
13.3 Gauss's Law for Electromagnetism in d Dimensions 170
13.4 Gauss's Law for Gravity in d Dimensions 171
13.5 Consistent Truncations 173
14 calN =1 Supergravity in 4 Dimensions 178
14.1 Rigid Supersymmetry 178
14.2 Supergravity 181
14.3 Vielbein-Spin Connection Formulation of General Relativity 183
14.4 calN=1 Supergravity in 4 Dimensions 185
15 KK Compactification of Supergravity Models 189
15.1 KK Reduction 190
15.2 calN=1 Supergravity Coupled to Matter 191
15.3 Supergravity Compactifications 194
15.4 11 Dimensional Supergravity 195
16 The Relativistic Point Particle 199
16.1 Relativistic Second Order Action 199
16.2 Quantum Field Theory in the Worldline Formalism 202
16.3 First Order Particle Action 203
16.4 Quantization of the Particle in the Light-Cone Gauge 205
17 Relativistic Strings 209
17.1 String Worldsheet and Tension 209
17.2 Induced Metric and the Nambu–Goto Action 210
17.3 The First Order Polyakov Action 212
17.4 Equations of Motion, Boundary Conditions and Constraints 213
17.5 Coupling of String to Background Fields 217
18 Light-Cone Gauge Strings and Quantization 220
18.1 Light-Cone Gauge 220
18.2 String Mode Expansions 222
18.3 Constraints and Hamiltonian 223
18.4 Quantization of String Modes 226
18.5 Light-Cone Gauge Quantization 227
19 D-Branes and Gauge Fields 232
19.1 The D-Brane Action 233
19.2 Chan–Paton Factors and Several D-Branes 238
19.3 Quantizing Open Strings on Dp-Branes 238
20 Electromagnetic Fields on D-Branes and calN=4 SYM. T-Duality of Closed Strings 244
20.1 Supersymmetric String Theory 244
20.2 D3-Brane Action and calN=4 SYM 245
20.3 Nonlinear Born–Infeld Action 247
20.4 Closed Strings on Compact Spaces 248
20.5 T-Duality of Closed Strings 251
21 T-Duality of Open Strings. M-Theory and the Duality Web 255
21.1 T-Duality of Open Strings 255
21.2 T-Duality with Chan–Paton Factors: Several D-Branes 257
21.3 Supergravity Actions 259
21.4 M-Theory 263
21.5 The String Duality Web 265
22 String Theory and Particle Physics 268
22.1 Dimensional Reduction on Compact Spaces 268
22.2 Calabi–Yau Compactification of String Theories 271
22.3 Intersecting D-Branes: Braneworld 273
22.4 Moduli Stabilization 274
23 Holography and the AdS/CFT Correspondence 276
23.1 AdS Space and Its Holography 276
23.2 Conformal Field Theories 279
23.3 AdS/CFT Motivation (Heuristic Derivation) 281
23.4 AdS/CFT Definition and Limits 284
23.5 Operator/State Map and GKPW Construction 285
23.6 Generalization to Non-conformal Theories: Gauge/Gravity Duality 288
Part III Introduction to String Cosmology 291
24 Problems of String Inflation 292
24.1 Moduli of Type IIB String Compactifications on CY3 293
24.2 Approximations for String Calculations of the Potential 296
24.3 Eta Problem in String Theory 297
24.4 Energy Scales for Most Controlled Approximations 298
24.5 Large Field Inflation 300
25 Problems of the Supergravity Approximation to String Inflation 302
25.1 Supergravity Plus Chiral Multiplet 302
25.2 D-Term Inflation 304
25.3 Field Redefinitions 306
25.4 Example with ?,?ll1 306
25.5 Special Embedding of Inflationary Potentials in Supergravity 309
26 Brane (-Antibrane) Inflation 313
26.1 Brane Probe Inflation 313
26.2 Brane-Antibrane Inflation: Flat Space Approximation 316
26.3 Brane-Antibrane Inflation in Compact Space 319
27 Braneworld Cosmology and the Israel Junction Conditions 323
27.1 Braneworld Cosmology in the Brane Formalism 324
27.2 Embedding Theory 325
27.3 Braneworld and Cosmology 327
27.4 Israel Junction Conditions 328
27.5 FLRW Cosmology 330
28 The KKLT Scenario for de Sitter Backgrounds in String Theory 333
28.1 Supersymmetric Vacua Are AdS 333
28.2 General Set-up for KKLT 335
28.3 Moduli Stabilization in KKLT 337
28.4 Compactification 339
28.5 de Sitter Vacua 340
29 The KKLMMT Scenario for Inflation and Generalizations 342
29.1 Simplified Model for KKLMMT 343
29.2 String Theory Example for KKLMMT Construction 346
29.3 Volume Stabilization and Problems 347
29.4 KKLMMT Generalization with Magnetic Flux 349
29.5 Type IIA Model Corresponding to KKLMMT 350
30 The Ekpyrotic Scenario 353
30.1 The Ekpyrotic Phase 354
30.2 Kinetic Phase 356
30.3 String Theory Model 359
30.4 Solving an Issue Related to the Null Energy Condition 361
30.5 Fluctuations in Ekpyrotic Models 364
31 The Cyclic and New Ekpyrotic Scenarios 367
31.1 The Cyclic Model 367
31.2 The New Ekpyrotic Cosmology 372
32 String Gas Cosmology: Basics and Brandenberger-Vafa Scenario 378
32.1 Hagedorn Temperature 378
32.2 3 Large Spatial Dimensions 380
32.3 String Equations of Motion 381
32.4 String Gas Cosmological Model 382
32.5 Cosmological Early Time Evolution 386
32.6 Moduli Stabilization 387
33 String Gas and Brane Gas Developments 390
33.1 Brane Gas 390
33.2 Cosmological Perturbations Generalities 392
33.3 Correlators from Thermodynamics 394
33.4 Thermodynamics for String Gas 396
33.5 String Gas Power Spectra and Tilts 398
34 Chameleon Scalars and String Theory 403
34.1 Chameleon (and Symmetron) Models 403
34.2 Thin-Shell Effect 406
34.3 String Theory Embedding 407
34.4 Experimental Constraints 409
35 Axion Inflation and Axion Monodromy from String Theory 413
35.1 Axions in Field Theory 413
35.2 Axions in String Theory 415
35.3 ``Racetrack'' with Two Axions 418
35.4 N-Flation 420
35.5 Axion Monodromy Inflation 421
35.6 Dante's Inferno 424
35.7 Phenomenology of Axion Monodromy Inflation 425
36 Fuzzy Dark Matter from String Theory 428
36.1 Fuzzy Dark Matter from String Theory 428
36.2 Axion Dynamics in the Expanding Universe 429
36.3 Fuzzy Dark Matter as a Nonrelativistic Quantum System 430
36.4 Superfluid Picture 431
36.5 Schrödinger–Poisson Equation and Spherical Soliton Solution 432
36.6 Observational Consequences 433
37 Holographic Cosmology 436
37.1 Generic Holographic Cosmology Map 436
37.2 Domain Wall/Cosmology Correspondence 438
37.3 Holographic Calculation 440
37.4 Phenomenological QFT Calculation 441
37.5 Time Dependent Field Theory Model: Top Down Holography 444
37.6 Spectrum of Fluctuations Going Through Singularity, from Holography 446
References 450
Index 454