305 Acceleration, 4D Supergravity 93 Corrections 96

305

Index a – type IIB 237 acceleration, 4D supergravity 93 black hole α corrections 96, 200, 291 – dark energy 286 Abelian Higgs model 123 – gauge theory 256 action blow-up inflation 103 – boundary 166 blue tilt 216, 218, 220 – Dirac–Born–Infeld (DBI) 36, B-mode polarization 147 53, 170 Bogoliubov parameter 165, 166, 254 – matrix membrane theory 240 bosonic – Nambu–Goto 13, 276 – massless fields 28 – Polyakov 13, 14, 19, 23 – strings, quantization 16 AdS/CFT correspondence, see gauge- – string theory 12 gravity duality bound states, formation 125 anisotropy 144 boundary conditions – semilocal strings 151 – action 166 – small-angle CMB 146 – primordial 161 Anti-de Sitter space 44, 98, 178, 182 – wavefunctional, bulk cosmology – unstable potentials 256 259 Anti-de Sitter spacetime 288 BPS D-branes 36, 38 antibranes 51 brane – vacuum energy 99 – annihilation 51 Atacama Cosmology Telescope (ACT) – fractional 178 147 –inflationmodels 50 axion field 136 – M2-, M5-branes 273 axion-dilaton 55 – space-filling, superstring breakage 140 b brane-antibrane inflation 50 background radiation, microwave 2 – slow-roll parameters 59, 61 balancing equation 292, 294 brane-world cosmology 39 baryon 136, 139, 150 breathing mode 94 – cosmic fluid component 4 bulk cosmology 257 BD state, see Bunch–Davies vacuum Bunch–Davies (BD) vacuum state state 163, 166 BICEP experiment 147 – deviation 176 Big-Bang – matrix 236 c – horizon problem 7 Calabi–Yau – flatness problem 7 – compactification 268 –model 1,7 – K3-fibered 107 – pp wave 236, 239 – racetrack inflation 100

Calabi–Yau manifolds 39, 53 – formation 124 – SU(3) structure 272 – gravity wave bursts 148 – throats 138 – lensing 148 – volume stabilization 63 – small-scale 126 Calabi–Yau orientifolds 40, 52, 53 cosmic string network 123, 124 – KKLMMT model 137 – bound states 142 Chan-Paton factors 22 – CMB 144 chaotic inflation 159 – KKLMMT model 137 closed bosonic string 15 – novel properties 140 – boundary conditions 25 – observation 143 – mass levels 17 – one-scale approximation 125 – massless excitations 19 – problems 142 – modular inflation 50, 90, 116 cosmology –spectrum 30 – bulk 257 – T-duality 30 – early universe 193 – Virasoro constraints 14 – ghost 286 CMB, see Cosmic microwave –standardmodel 1 background – string cosmology 158 Coleman–Weinberg correction 68 – string gas cosmology 193 compactifications cosmological – Calabi–Yau manifolds 39, 268 – constant 41, 58, 285, 287 – D3/D7-branes 70 – perturbations 194, 212, 218 – Kaluza–Klein 38 – red-shift 130 – M-theory 269, 284, 295 cycloops 143 – string tension 129 – warped geometries 178 d comoving dark energy 285 – coordinates 194 – cosmic fluid component 5 –fluidelements 3 – holographic 286 – frame 6, 10 – Neutrino 286 – mode 161, 162 – scale, fine-tuning 287 – momentum 167 dark matter, cosmic fluid component –observer 6 5 – scale 210 DBI inflation 73, 80, 169 conifold, warped deformed 178 – non-Gaussianity 171 cosmic fluid, components 4 – warped geometry, observation cosmic microwave background (CMB) 182 6, 144, 157 D-branes 36 – anisotropy 145 – breakage 135 – B-modes 147 –charge 38 – non-Gaussianities 169 – DBI action 37, 170 – oscillatory primordial power – Dirichlet-boundary conditions spectrum 167, 194 15, 16 – small-angle, observations 146 – gauge-gravity dualities 44 – transplanckian studies 161 – symmetric torus 79 – warped geometry, observation – tachyonic decay 137 182 – T-duality 31 cosmic string –warpedthroat 79 – infinitely extended 274 – Wess–Zumino coupling 283 – heterotic, production 282 – wrapped branes 81 – stability 278 D0-branes 233 – tensions 275 D3/D3-brane inflation 50 cosmic string loop 123, 274 – volume stabilization 63 Index 307

–warped 59 – vacuum 291 D3/D7-brane inflation 67 – winding strings 202 – moduli stabilization 71 energy production, gauge theory D-celleration mechanism 170 253 de Sitter space 162 energy-momentum fluctuations 213 de Sitter uplifting 58 energy-momentum tensor 3, 213, dielectric effect, baryon decay 139 219, 247 defects, symmetry breaking 122 – dark energy 288 density perturbations 217, 221 entropy, string gas 215 dilaton 50, 201 expansion 8 – gravity equations 199 – α 96 – stabilization 204, 207 – accelerated 92, 193 th 11 dimension 268 –inflation 8,47 Dirac–Born-Infeld inflation, see DBI – rate 194 inflation – small fluctuations 9 Dirichlet branes, see D-branes – string loop 96 Dirichlet boundary conditions, open extension, self-adjoint 260 strings 16 Discrete Light Cone Quantization, see f DLCQ fermions DLCQ matrix theory 232 – boundary conditions 24 domain walls 136, 279 – Majorana 23 Dp-branes 16 – Majorana–Weyl 249 – effective actions 37, 53 Fiber inflation 107 – wrapped 81 fixed points 36 D-strings 131 fluctuations 9, 102, 194, 213 – binding 132 – energy-momentum 213 – cosmic 283 – gravitational 219 4D-string vacua 90 4D-supergravity, acceleration 93 – Hubble radius 210 D-term inflation model, hybrid 69 – inflation 11, 102, 117 dual gauge theory 248, 258 – scalar metric 218, 220 duality – spectrum 10, 217 –gauge-gravity 44 – squeezing 222 – string breakage 135 – trans-Planckian problem 196 Dvali–Gabadaze–Porrati (DGP) model – warped deformed conifold 286 179 flux compactification, M-theory 269 e fluxes effective field theory (EFT) 157 – Calabi–Yau manifolds 56 – boundaries 164 – 3-form 71, 73, 291, 292 – oscillation 169 – G-flux 271 e-foldings 2, 78, 102, 103, 115 free energy, string gas 213 EFT, see effective field theory Friedmann equation 3 Einstein equations 2, 19, 161, 179, Friedmann–Robertson–Walker (FRW) 288 cosmology 285 Einstein-frame action 21, 258 Friedmann–Robertson–Walker (FRW) energy density 3, 89, 141, 212 metric, see Robertson–Walker –darkenergy 5 metric – inflation 103 FRW cosmology, see Friedmann– –inflaton 47 Robertson–Walker cosmology – particles 263 F-strings 128, 132 –universe 4 fuzzy ellipsoids 240 308 Index

g holographic dark energy 286 galaxy formation 6 holography 231 gauge theory 242 homogeneous modes 260 – black hole 256 Hubble – dual 248 – expansion 193 – energy production 253 –law 2,7 – particle production 254, 262 – parameter 2, 5, 47, 163, 165, – time evolution 243 182 – unstable potentials 256 – radius 194, 195, 210 – vacuum state 247 gauge-gravity duality 44, 242, 247 i gaugino potential, dilaton stabilization inflation 7, 47, 157 209 – analysis, approximations 92 gauge-invariant perturbations 171, – blow-up mode 103 172, 174 – chaotic 159 G-flux 271, 294 – D3/D3brane,warped 59 ghost cosmology 286 – D3/D7brane 67 graceful exit 93 – DBI 73, 80 grand unified theories 267 – de Sitter 58 gravitino 269 – early universe 193 gravitational constant 123 – e-fold parameter 115 gravitational lensing 145 – Fiber 107 gravitational wave 77, 126, 217 – fluctuation 11, 196 – bursts 148 – gravitational waves 77 – detectable 299 – hybrid 131 – primordial 159, 187 –hybridD-term 69 – spectrum 219 – initial conditions 160 – squeezing 220 – kinetic terms 111 graviton 130 –k-inflation 74 gravity –Kählermoduli 99 – gravity equations 199 – moduli stabilization 49 – gauge-gravity dualities 44 – multibrane 296 – modified 286 – non-Gaussiantiy 175 Green’s function method 66 – power-law 298, 299 Green–Schwarz (GS) formalism 23 – racetrack 100 GSO projection (Gliozzi–Scherk–Olive – scalar field matter 195 projection) 25 – slow-roll 47, 59, 61, 111, 158 GUT unification, see grand unified – superstrings 131 theories – UV-sensitivity 48 – volume model 117 h – warped 59, 133 Hagedorn temperature 43, 198 inflaton 49 Hagedorn phase 133, 199, 223 – canonical normalization 62, Hankel functions 251 75, 112, 170, 298 Harrison–Zel’dovich spectrum 11 – closed-string moduli 90, 116 heterotic M-theory 35, 267, 268 – cosmic string formation 133, – multibrane inflation 296 282 – square potential 293 –energydensity 47 – vacuum energy 293 – higher derivative terms 74 heterotic string theory 267, 289 – kinetic term 105 – vacuum energy 291 – Lagrangian 73, 111 heterotic superstring theory 27, 206, –mass 72 224 – multibrane inflation 297, 298 Index 309

– perturbations 12 LISA experiment (Laser – shift symmetry 73 Interferometer Space Antenna) inhomogenous modes 262 149 instantons, multibrane inflation loops 297, 298 – corrections 109, 110 intercommutation – see also cosmic string loops – loop formation 124 LVS (largevolume scenario) 98 – reduced rates 140, 149 Lyth bound 78 k m K3 fibration 107 mass Kähler cone 113 –inflaton 72 Kähler manifolds 39 – levels, closed bosonic strings Kähler moduli 55, 94 17 –fluxes 56 massless – blow-up mode inflation 103 – axion, removal 279 – racetrack inflation 100 – bosonic fields 28 Kähler moduli inflation, see blow-up – closed-string excitations 19 inflation – modes 206 Kähler potential, tree-level 56 matrix Big-Bang 236 Kaiser–Stebbins effect 145 matrix membrane theory 235 Kaluza–Klein compactifications 38 – Lagrangian density 238 Kasner metric 245 matrix string theory 232 kinetic terms, inflationary analysis – DLCQ 232 111 – pp-wave 236, 239 k-inflation 74 matrix theory 231, 232 KKLMMT model 137 matter-radiation equality 102 KKLT scenario 98 M2-branes 273 Klebanov–Strassler, warped deformed – cosmic string tensions 275 conifold 178 – quantum stability 281 Klein–Gordon equation, free scalar – worlvolume 274 field 210 M5-branes 273 KS throat 184 – cosmic string tensions 276 – see also Klebanov–Strassler – multibrane inflation 296 – stability 278 l – quantum stability 281 Lagrangian 41, 73, 94, 240 – worlvolume 274 – DBI inflation, non-Gaussianity microwave background radiation 2, 171 6 – field theory 123 Minkowski spacetime 19, 23, 39, – matrix membrane theory 237 288 – Super–Yang–Mills (SYM) theory modular inflation 50 258 moduli 42 – Yang–Mills (YM) theory 249 – complex moduli 55 large volume scenario, see LVS – geometrical 204 lensing –Kählermoduli 55 – cosmic string loops 148 – massless string states 207 – gravitational 145 – stabilization 43, 49, 52, 71, 94, – junction, three-way 150 203 light-front time 243 – type IIB 94 LIGO (Laser Interferometer – volume modulus 57 Gravitational-Wave Observatory) monopole 143, 150 148 motion, equations 91, 250, 254 310 Index

M-theory 28, 33, 267 p – compactifications 269, 284, particle production, gauge theory 295 254, 262 – geometry 270 PBH transformations, see Penrose– – heterotic M-theory 35, 267, Brown–Henneaux transformations 268 Penrose–Brown–Henneaux (PBH) –M2andM5brane 35 transformations 246 – type IIA superstring theory perturbations 34, 232 – Big-Bang model, initial – web of dualities 33 perturbations 7 multibrane inflation 296 – cosmological 194, 217 multifield effects 175 – density 217 – evolution 210 n – gauge-invariant 171, 172, 174 Nambu–Goto action 13, 275, 276 –inflaton 12 necklaces, baryons 150 – power spectrum 164 Neumann boundary conditions, open – primordial 117, 143, 165 strings 15, 32 – scalar 77, 115, 217 Neutrino dark energy 286 –string 17 Neveu–Schwarz 23 – string-sourced 146, 147 – boundary conditions 25 – tensor 77, 115, 147 – three-form 291 – vacuum 210, 212 –two-form 90 – vector 147 New Physics Hypersurface (NPH) Planck time 167 164 polar bear experiment 147 – oscillations 169 polarization, B-mode 147 non-Gaussianity 159, 222 Polyakov action 13 – CMB 169 power spectrum of fluctuations 10 – DBI inflation 171 – primordial, oscillatory 167 – shape 173 – scalar metric fluctuations 12, – WMAP3 data 176 218 NPH, see New Physics Hypersurface pp-waves 239 nucleosynthesis 6 (p,q)-strings 132, 150, 239 o – baryon decay 137, 139 open bosonic string 15 pulsar, timing 145 – Dirichlet and Neumann- punctures 19 boundary conditions 15 – fermion boundary conditions q 24 quantum – inflation 50, 90 – stability, M2,- M5-branes 281 – T-duality 31 – theory, Weyl-invariant 20 – thermodynamics 43 – Virasoro constraints 14 r O-planes see orientifolds racetrack inflation 100 orbifolds 41 radiation orientifolds 40 – cosmic fluid component 4 – Calabi–Yau, type IIB 52 – phase, transition 200 – KKLMMT model 137 radiation-matter oscillation – crossover 6 – primordial power spectrum – equality 5, 102 167 radion, stabilization 205 – wavefunctional 252 Ramond boundary conditions 24 Index 311

Ramond–Neveu–Schwarz (RNS) – α parameter, see length formalism 23 – bound states 141 Ramond–Ramond (RR) flux 179 –boundaries 18 Randall–Sundrum (RS) model 179 – breakage 134 red tilt 12, 216, 219, 221 –closed 15 Robertson–Walker (RW) metric 2, 3, – cosmic 121, 272, 274, 275 9 – cosmology 158 – coupling constant 18, 20, 21, s 202, 233, 236, 237, 240 scalar field matter 195 – dualities 28 scalar perturbations 77, 115, 217 – fundamental 128 – gauge-invariant variables 174 – heterotic 272 scalar potential 101, 108 – length 29, 34, 233, 243 – blow-up mode inflation 104 – local 122 Second Superstring Revolution 128 – long 123 self-duality 29, 53 – loop 123, 124, 202, 274 singularity 199, 241 – mass 202, 204 – AdS/CFT correspondence 242 – moduli 42, 89 – big bang 197 –oriented 22 – bulk cosmology 259 –open 15 – curvature 241, 246 – perturbation 17, 146, 147 – null 231, 232, 241, 243 – scale, lowering 273 – spacelike 231, 245, 248, 256 – semilocal 123, 151 – supergravity 255 – states 198 slow roll 8, 12 – superconducting 124 – generalization 76 – tension 123, 129 – inflation 47, 101, 111, 158, – thermodynamics 212 300 – twisted, untwisted 42 – large-field inflationary models –unoriented 22 106 – wiggliness 127 – naturalness 106 – winding 200, 202 – parameters 113, 114 – world-sheet 13, 18, 234 – warped inflation 59, 61 – Yang–Mills (YM) theory 234 small-scale structures 126 S-duality 28, 32 sound speed 6 string gas South Pole Telescope (SPT) 147 – modes 203 spacetime – source term 205 – Anti-de Sitter 288 – superposition 204 – curved, massless closed-string string gas cosmology 193 excitations 20 – dilaton stabilization 208 – inflationary cosmology 194, – dynamical evolution 199 196 – principles 197 – matrix theory 236, 241 string-loop corrections 96 – Minkowski 19, 23, 39, 288 string theory – string gas cosmology 211 – bosonic 12 spatial dimensions, string gas – Calabi–Yau manifolds 39 cosmology 200 – observations 157 spectral index 10, 70, 103, 183, 184 – heterotic 35, 205, 206, 267, Spider experiment 147 289 squeezing factor 220 – M-theory 35, 267 standard model of cosmology 1, – inflation 49, 89, 117 151, 268 –orbifolds 41 string – perturbative 13, 241 312 Index

– type IIA 233 –energydensity 76 – type IIB, matrix theory 235 – energy-momentum 3, 214, – type IIB, moduli stabilization 219, 247, 288 52 – mode spectrum 220 –unoriented 22 – perturbations 77, 115, 147 string vacuum 90 –spectralindex 12 strong-weak coupling duality, see under – stress energy 248 S-duality tensor-to-scalar SU(3) 272 – fluctuation 219 supergravity 29, 64, 242 –ratio 77 – 4D, acceleration 93 thermalization, gauge theory 255 –expansion 92 thermodynamics –M-theory 35 – open bosonic strings 43 – singularity 255 – string gas cosmology 212 – type IIB 52 time 231 superpotential 208 – conformal 10, 217 – corrections 97 – evolution, gauge theory 243 –4Dfields 95 topological defect 122 – inflaton dependance 64 torus, symmetric 79 superstrings 23, 121 trans-Planckian physics 160, 196 – CMB 144 tree-level Kähler potential 56 – cosmic 127, 187 – GSO projection 25 u – heterotic model 27 U-duality 33 – inflation 131 universe – macroscopic 127 – development 6, 122, 199, 223 – observation 143 – early 193 – S-duality 32 – energy content 4 – stability 134 – four-dimensional, flat 194 – T-duality 32 – present-day structure 1 – type IIA, M-theory 34 UV DBI inflation 81 – type IIA and type IIB models UV-sensitivity, inflation 48 26 –typeImodel 26 v – world-sheet supersymmetry vacuum 23 –4Dvacua 90 supersymmetry 23, 91, 236 – energy 58, 287, 290, 291, 293 – breaking 98, 290, 293 – perturbations 210, 212 – dark energy 288 – gauge theory 247 Super–Yang–Mills (SYM) theory 258 vector perturbations 147 SYM theory, see Super–Yang–Mills Virasoro constaints 14 theory volume inflation model 117 symmetry breaking 122 volume modulus, nonperturbative corrections 57 t vortons 143 tachyon 37, 137, 206, 283 target space duality, see under T-duality w T-duality 28, 29, 197, 198 warp factor 54, 61, 129, 170, 183, –closedstrings 30 294 –openstrings 31 – KS throat 184 – superstring theories 32 – M-theory 270 tension, strings 129, 275 – warped deformed conifold tensor 213 181 Index 313

–warpedthroat 62 WMAP (Wilkinson Microwave warped brane-antibrane inflation 59 Anisotropy Probe) 4, 70, 146, 172, warped geometry 178, 183, 293 175 warped throat geometry 61, 130, world-sheet 133, 177 – of the string 13, 18, 234 – AdS throat 184 –metric 13 – D3-branes 79 – topologies 18 – KS throat 184 – supersymmetry 23 warped volume 66 worldvolume wavefunctional 251, 252 –fluxes,D3/D7-brane inflation – boundary conditions 259 67 – homogenous modes 261 – M2-brane, M5-brane 274 Wentzel–Kramers–Brillouin (WKB) wrapped branes 81, 273, 279 wavefunction 260 Wentzel–Kramers–Brillouin (WKB) y wavefunction, homogenous modes Yang–Mills (YM) theory 233 261 – Lagrangian 249 wiggliness 127 – twist sector 234 winding 198 YM theory, see Yang–Mills theory – number 30, 82, 204 – modes 198, 200, 202 z WKB wavefunction, see Wentzel– zero vacuum energy 293

Kramers–Brillouin wavefunction 2-symmetry 35, 137, 270