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 String Cosmology. Edited by Johanna Erdmenger Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40862-7 306 Index 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 –