100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

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412 M. Bojowald4. D. N. Spergel et al. Astrophys. J. Suppl. 148, 175 (2003), [astro-ph/0302209].5. T. Padmanabhan, this volume.6. S. W. Hawking and R. Penrose, Proc. Roy. Soc. Lond. A 314, 529–548 (1970).7. A. Friedmann, Z. Phys. 10, 377–386 (1922).8. A. D. Linde, Phys. Lett. B 129, 177–181 (1983).9. A. Borde, A. H. Guth and A. Vilenkin, Phys. Rev. Lett. 90, 151301 (2003),[gr-qc/0110012].10. B. S. DeWitt, Phys. Rev. 160, 1113–1148 (1967).11. D. L. Wiltshire, in Cosmology: The Physics of the Universe, Ed. B. Robson,N. Visvanathan and W. S. Woolcock (World Scientific, Singapore, 1996), p.473–531, [gr-qc/0101003].12. A. Vilenkin, Phys. Rev. D 30, 509–511 (1984).13. J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2960–2975 (1983).14. C. Rovelli, Living Reviews in Relativity 1, 1 (1998), [gr-qc/9710008],http://www.livingreviews.org/Articles/Volume1/1998-1rovelli.15. T. Thiemann, Introduction to Modern Canonical Quantum General Relativity,[gr-qc/0110034].16. A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 21, R53–R152(2004), [gr-qc/0404018].17. A. Ashtekar, this volume.18. A. Ashtekar, Phys. Rev. D 36, 1587–1602 (1987).19. J. F. Barbero G., Phys. Rev. D 51, 5507–5510 (1995), [gr-qc/9410014].20. C. Rovelli and L. Smolin, Nucl. Phys. B 331, 80–152 (1990).21. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão and T. Thiemann, J.Math. Phys. 36, 6456–6493 (1995), [gr-qc/9504018].22. C. Rovelli and L. Smolin, Phys. Rev. D 52, 5743–5759 (1995).23. H. Sahlmann, Some Comments on the Representation Theory of the AlgebraUnderlying Loop Quantum Gravity, [gr-qc/0207111].24. H. Sahlmann, When Do Measures on the Space of Connections Support theTriad Operators of Loop Quantum Gravity?, [gr-qc/0207112].25. A. Okolow and J. Lewandowski, Class. Quantum Grav. 20, 3543–3568 (2003),[gr-qc/0302059].26. H. Sahlmann and T. Thiemann, On the superselection theory of the Weyl algebrafor diffeomorphism invariant quantum gauge theories, [gr-qc/0302090].27. C. Fleischhack, Representations of the Weyl Algebra in Quantum Geometry,[math-ph/0407006].28. C. Rovelli and L. Smolin, Nucl. Phys. B 442, 593–619 (1995), [grqc/9411005],Erratum: Nucl. Phys. B 456 (1995) 753.29. A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55–A82 (1997),[gr-qc/9602046].30. A. Ashtekar and J. Lewandowski, Adv. Theor. Math. Phys. 1, 388–429 (1997),[gr-qc/9711031].31. T. Thiemann, Class. Quantum Grav. 15, 839–873 (1998), [gr-qc/9606089].32. T. Thiemann, Class. Quantum Grav. 15, 1281–1314 (1998), [gr-qc/9705019].33. M. Bojowald, Quantum Geometry and Symmetry, PhD thesis, RWTHAachen, 2000, published by Shaker-Verlag, Aachen.
Loop Quantum Cosmology 41334. M. Bojowald and H. A. Kastrup, Class. Quantum Grav. 17, 3009–3043(2000), [hep-th/9907042].35. M. Bojowald, Class. Quantum Grav. 21, 3733–3753 (2004), [gr-qc/0407017].36. A. Ashtekar, M. Bojowald and J. Lewandowski, Adv. Theor. Math. Phys. 7,233–268 (2003), [gr-qc/0304074].37. A. Ashtekar, S. Fairhurst and J. Willis, Class. Quant. Grav. 20, 1031–1062(2003), [gr-qc/0207106].38. W. Thirring and H. Narnhofer, Rev. Math. Phys. SI1, 197–211 (1992).39. M. Bojowald and H. A. Morales-Técotl, in Proceedings of the Fifth MexicanSchool (DGFM): The Early Universe and Observational Cosmology, Lect.Notes Phys. 646, Springer-Verlag, 2004, p. 421–462, [gr-qc/0306008].40. M. Bojowald, Class. Quantum Grav. 19, 2717–2741 (2002), [gr-qc/0202077].41. M. Bojowald, Phys. Rev. Lett. 86, 5227–5230 (2001), [gr-qc/0102069].42. M. Bojowald, Class. Quantum Grav. 18, L109–L116 (2001), [gr-qc/0105113].43. D. Giulini, C. Kiefer, E. Joos, J. Kupsch, I. O. Stamatescu and H. D. Zeh,Decoherence and the Appearance of a Classical World in Quantum Theory,Springer, Berlin, Germany, 1996.44. G. M. Hossain, Class. Quantum Grav. 21, 179–196 (2004), [gr-qc/0308014].45. K. Noui, A. Perez and K. Vandersloot, Phys. Rev. D 71, 044025 (2005),[gr-qc/0411039].46. A. Ashtekar, T. Pawlowski and P. Singh, Quantum nature of the big bang:An analytical and numerical study, in preparation.47. M. Bojowald and G. Date, Class. Quantum Grav. 21, 121–143 (2004), [grqc/0307083].48. M. Bojowald, Phys. Rev. Lett. 87, 121301 (2001), [gr-qc/0104072].49. M. Bojowald, Gen. Rel. Grav. 35, 1877–1883 (2003), [gr-qc/0305069].50. D. Cartin, G. Khanna and M. Bojowald, Class. Quantum Grav. 21, 4495–4509 (2004), [gr-qc/0405126].51. D. Cartin and G. Khanna, Phys. Rev. Lett. 94, 111302 (2005), [grqc/0501016].52. M. Bojowald, Phys. Rev. Lett. 95, 061301 (2005), [gr-qc/0506128].53. M. Bojowald, Phys. Rev. D 64, 084018 (2001), [gr-qc/0105067].54. M. Gaul and C. Rovelli, Class. Quantum Grav. 18, 1593–1624 (2001), [grqc/0011106].55. M. Bojowald, Class. Quantum Grav. 19, 5113–5130 (2002), [gr-qc/0206053].56. M. Bojowald, in Proceedings of the International Conference on Gravitationand Cosmology (ICGC 2004), Cochin, India, Vol. 63, Pramana, 2004, p. 765–776, [gr-qc/0402053].57. A. Ashtekar, M. Bojowald and J. Willis, in preparation.58. J. Willis, On the Low-Energy Ramifications and a Mathematical Extensionof Loop Quantum Gravity, PhD thesis, The Pennsylvania State University,2004.59. M. Bojowald, P. Singh and A. Skirzewski, Phys. Rev. D 70, 124022 (2004),[gr-qc/0408094].60. P. Singh and A. Toporensky, Phys. Rev. D 69, 104008 (2004), [grqc/0312110].
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Published byWorld Scientific Publis
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viA. Ashtekarof space-time that eme
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viiiA. AshtekarGravitational waves
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xA. Ashtekarhappy, schizophrenic at
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xviContents9. Receiving Gravitation
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4 J. Stachel(2) the change over tim
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6 J. StachelFig. 2respectively. Fur
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8 J. Stachelof string theory, M-the
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10 J. StachelLogically, it would se
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12 J. Stachelupon by no (net) exter
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14 J. Stachelof the incompatibility
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16 J. Stachelis an important differ
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18 J. Stachelbetween physical conce
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20 J. Stachel10. Four-Dimensional F
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22 J. Stachelderivative of the metr
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24 J. Stachel(b) General relativity
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26 J. Stachelfour-dimensional analo
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28 J. Stachelply the lessons learne
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30 J. Stachelmanifold appropriate f
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32 J. Stachelwhich merely defines t
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34 J. Stacheldynamical process as a
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36 J. Stachel9. J. Stachel, Special
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Part IIEinstein’s UniverseRamific
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40 H. Nicolai• Higher dimensions
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42 H. Nicolaiadvance, and possibly
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44 H. NicolaiBianchi identities are
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46 H. NicolaiIt does not appear pos
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48 H. NicolaiThe other SL(2, R), of
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50 H. Nicolai3.1. BKL dynamics and
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52 H. Nicolaidegrees of freedom, th
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54 H. Nicolaiin the valley. The Ham
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56 H. NicolaiThe main feature of th
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58 H. Nicolai4. Basics of Kac Moody
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60 H. Nicolaifor indefinite A. It i
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62 H. NicolaiThe level l = 0 sector
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64 H. NicolaiConsequently, the repr
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66 H. Nicolaiwhere the abelian part
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68 H. Nicolaiconstant momenta Π yi
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70 H. Nicolaiσ-model side is suppo
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72 H. NicolaiReferences1. H.A. Buch
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74 H. Nicolai44. G. Neugebauer and
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CHAPTER 3THE NATURE OF SPACETIME SI
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78 A. D. Rendallspacetime to define
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80 A. D. RendallOne of the most imp
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82 A. D. Rendalltheorems was an elu
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84 A. D. Rendallsymmetric solution
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86 A. D. Rendallback into a curvatu
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88 A. D. Rendallspace and there are
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The Nature of Spacetime Singulariti
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CHAPTER 4BLACK HOLES - AN INTRODUCT
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Black Holes 95It follows that ˙v d
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Black Holes 973221100-1-1-2-200-5-3
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Black Holes 99calculation of the de
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Black Holes 101family of null geode
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Black Holes 105(3) Ω is positive o
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Black Holes 107In dimension 3 + 1 t
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Black Holes 109A fundamental theore
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Black Holes 111(4) The Kerr black h
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Black Holes 113˚g ab =˚g ab (x a
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Black Holes 115It is a folklore the
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Black Holes 117⃗x 4 = −⃗x 3
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Black Holes 119Work partially suppo
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Black Holes 121totically flat space
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Black Holes 12376. R.C. Myers and M
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The Physical Basis of Black Hole As
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Probing Space-Time Through Numerica
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CHAPTER 7UNDERSTANDING OUR UNIVERSE
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Understanding Our Universe: Current
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CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
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Was Einstein Right? 207We begin in
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Was Einstein Right? 20910 -810 -9E
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Was Einstein Right? 211On this 100t
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Was Einstein Right? 213The SME and
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Was Einstein Right? 215where d is t
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Was Einstein Right? 217of VLBI data
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Was Einstein Right? 219milliarcseco
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Was Einstein Right? 2215. Gravitati
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Was Einstein Right? 223be measured
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Was Einstein Right? 22510. J. G. Wi
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Was Einstein Right? 22761. C. M. Wi
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Receiving Gravitational Waves 229th
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Receiving Gravitational Waves 231gr
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Receiving Gravitational Waves 233Th
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Receiving Gravitational Waves 235We
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Receiving Gravitational Waves 23719
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Receiving Gravitational Waves 239th
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Receiving Gravitational Waves 241to
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Receiving Gravitational Waves 243In
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Receiving Gravitational Waves 245
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Receiving Gravitational Waves 247a
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Receiving Gravitational Waves 249ab
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Receiving Gravitational Waves 251Fi
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Receiving Gravitational Waves 253Eq
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Receiving Gravitational Waves 255In
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CHAPTER 10RELATIVITY IN THE GLOBAL
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Relativity in the Global Positionin
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Part IIIBeyond EinsteinUnifying Gen
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CHAPTER 11SPACETIME IN SEMICLASSICA
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Spacetime in Semiclassical Gravity
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CHAPTER 12SPACE TIME IN STRING THEO
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Space Time in String Theory 313limi
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Space Time in String Theory 315luti
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Space Time in String Theory 317In s
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Space Time in String Theory 319of t
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Space Time in String Theory 321an o
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Space Time in String Theory 323arbi
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Space Time in String Theory 325an e
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Space Time in String Theory 327in a
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Space Time in String Theory 329doma
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Space Time in String Theory 331a tu
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Space Time in String Theory 333bran
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Space Time in String Theory 335is a
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Space Time in String Theory 337thes
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Space Time in String Theory 339The
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Space Time in String Theory 341gene
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Space Time in String Theory 343are
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Space Time in String Theory 345tion
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Space Time in String Theory 34723.
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Space Time in String Theory 34955.
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Gravity, Geometry and the Quantum 3
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Page 379 and 380: Gravity, Geometry and the Quantum 3
Page 395 and 396: £¢¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
Page 401 and 402: Loop Quantum Cosmology 383inflation
Page 403 and 404: Loop Quantum Cosmology 385gravitati
Page 405 and 406: Loop Quantum Cosmology 387Secondly,
Page 407 and 408: Loop Quantum Cosmology 389sically d
Page 409 and 410: Loop Quantum Cosmology 391states an
Page 411 and 412: Loop Quantum Cosmology 393represent
Page 413 and 414: Loop Quantum Cosmology 3954.2.1. Di
Page 415 and 416: Loop Quantum Cosmology 397question
Page 417 and 418: Loop Quantum Cosmology 399exist. Th
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Page 421 and 422: Loop Quantum Cosmology 403λ max or
Page 423 and 424: Loop Quantum Cosmology 405This happ
Page 425 and 426: Loop Quantum Cosmology 407Loop quan
Page 427 and 428: Loop Quantum Cosmology 409to obtain
Page 429: Loop Quantum Cosmology 411familiar
Page 433 and 434: CHAPTER 15CONSISTENT DISCRETE SPACE
Page 435 and 436: Consistent Discrete Space-Time 417v
Page 437 and 438: Consistent Discrete Space-Time 419I
Page 439 and 440: Consistent Discrete Space-Time 421a
Page 441 and 442: Consistent Discrete Space-Time 423F
Page 443 and 444: Consistent Discrete Space-Time 4250
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Page 447 and 448: Consistent Discrete Space-Time 429i
Page 449 and 450: Consistent Discrete Space-Time 431a
Page 451 and 452: Consistent Discrete Space-Time 433n
Page 453 and 454: Consistent Discrete Space-Time 435t
Page 455 and 456: Consistent Discrete Space-Time 437w
Page 457 and 458: Consistent Discrete Space-Time 439f
Page 459 and 460: Consistent Discrete Space-Time 441(
Page 461 and 462: Consistent Discrete Space-Time 443R
Page 463 and 464: CHAPTER 16CAUSAL SETS ANDTHE DEEP S
Page 465 and 466: Causal Sets and the Deep Structure
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Causal Sets and the Deep Structure
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CHAPTER 17THE TWISTOR APPROACH TOSP
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The Twistor Approach to Space-Time
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INDEXσ models, 57, 65, 693+1 formu
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Index 509inflation, 383, 385-387, 4
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