Classical and quantum features of the mixmaster singularity

International Journal of Modern Physics A

Volumn 23, Issue 16-17, 2008, Pages 2353-2503

  Montani, Giovanni ^a,b   Battisti, Marco Valerio ^a   Benini, Riccardo ^a   Imponente, Giovanni ^b,c  

^a ICRANET   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c MUSEO STORICO DELLA FISICA E CENTRO STUDI E RICERCHE ENRICO FERMI   (Italy)

Author keywords

Early cosmology; Primordial chaos; Quantum dynamics

Indexed keywords

EID: 49449089317     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0217751x08040275     Document Type: Review

References (520)

1. M. E. D. T. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).
2. A. J. Accioly, A. N. Vaidya and M. M. Som, Phys. Rev. D 28, 1853 (1983).
3. P. J. Adams, R. W. Hellings, R. L. Zimmerman, H. Farhoosh, D. I. Levine and S. Zeldich, Astrophys. J. 253, 1 (1982).
4. Y. Aizawa, N. Koguro and I. Antoniou, Prog. Theor. Phys. 98, 1225 (1997).
5. S. Alexandrov, Class. Quantum Grav. 17, 4255 (2000), arXiv:gr-qc/0005085.
6. S. Alexandrov and D. Vassilevich, Phys. Rev. D 64, 044023 (2001), arXiv:grqc/0103105.
7. G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos and D. V. Nanopoulos, Mod. Phys. Lett. A 12, 2029 (1997), arXiv:hep-th/9701144.
8. L. Andersson, H. van Elst, W. C. Lim and C. Uggla, Phys. Rev. Lett. 94, 051101 (2005), arXiv:gr-qc/0402051.
9. D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Steklov Inst. Math., Vol. 90 (1967) [MathSciNet, MR224110, American Mathematical Society, 1969].
10. P. S. Apostolopoulos, Class. Quantum Grav. 20, 3371 (2003).
11. P. S. Apostolopoulos, Gen. Relativ. Gravit. 37, 937 (2005), arXiv:gr-qc/0407040.
12. P. S. Apostolopoulos, Class. Quantum Grav. 22, 4425 (2005).
13. P. S. Apostolopoulos, Class. Quantum Grav. 22, 323 (2005).
14. P. S. Apostolopoulos and M. Tsamparlis, Gen. Relativ. Gravit. 35, 2051 (2003), arXiv:gr-qc/0305017.
15. G. B. Arfken, H. J. Weber and L. Ruby, Mathematical Methods for Physicists, Vol. 64 (American Association of Physics Teachers, 1996).
16. J. Argyris, I. Andreadis and C. Ciubotariu, Chaos Soliton Fract. 9, 1813 (1998).
17. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin, 1989).
18. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
19. R. Arnowitt, S. Deser and C. W. Misner, The dynamics of general relativity, Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, 1962), Chapter 7, pp. 227-265, arXiv:gr-qc/0405109.
20. E. Artin, Ein Mechanisches System mit Quasi-ergodischen Bahnen: Collected Papers, eds. S. Lang and J. T. Tate (Addison-Wesley, 1965).
21. A. Ashtekar, M. Bojowald and J. Lewandowski, Adv. Theor. Math. Phys. 7, 233 (2003), arXiv:gr-qc/0304074.
22. A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 21, R53 (2004), arXiv:grqc/0404018.
23. A. Ashtekar, T. Pawlowski and P. Singh, Phys. Rev. Lett. 96, 141301 (2006), arXiv:gr-qc/0602086.
24. A. Ashtekar, T. Pawlowski and P. Singh, Phys. Rev. D 73, 124038 (2006), arXiv:grqc/0604013.
25. A. Ashtekar and J. Samuel, Class. Quantum Grav. 8, 2191 (1991).
26. A. Ashtekar and J. Stachel (eds.), Conceptual Problems of Quantum Gravity (Birkhäuser, 1991).
27. M. Bachmann and H.-J. Schmidt, Phys. Rev. D 62, 043515 (2000), arXiv:grqc/9912068.
28. R. Bali and V. Chand Jain, Astrophys. Space Sci. 262, 145 (1998).
29. C. B. Balogh, SIAM J. Appl. Math. 15, 1315 (1967).
30. A. Banerjee, B. Bhui and S. Chatterjee, Astrophys. J. 358, 23 (1990).
31. J. Barrow, Chaotic behavior and the Einstein equations, Classical General Relativity, eds. W. B. Bonnor, J. N. Islam and M. A. H. MacCallum (Cambridge University Press, Cambridge, 1984), p. 26.
32. J. D. Barrow, Phys. Rev. Lett. 46, 963 (1981).
33. J. D. Barrow, Phys. Rep. 85, 1 (1982).
34. J. D. Barrow, Can. J. Phys. 64, 152 (1986).
35. J. D. Barrow, Phys. Rev. D 51, 3113 (1995).
36. J. D. Barrow, Phys. Rev. D 55, 7451 (1997), arXiv:gr-qc/9701038.
37. J. D. Barrow, P. G. Ferreira and J. Silk, Phys. Rev. Lett. 78, 3610 (1997), arXiv:astroph/9701063.
38. J. D. Barrow, Y. Gaspar and P. M. Saffin, Class. Quantum Grav. 17, 1435 (2000), arXiv:gr-qc/9905100.
39. J. D. Barrow, R. Juszkiewicz and D. H. Sonoda, Mon. Not. R. Astron. Soc. 213, 917 (1985).
40. J. D. Barrow and R. A. Matzner, Phys. Rev. D 21, 336 (1980).
41. J. D. Barrow and D. H. Sonoda, Phys. Rep. 139, 1 (1986).
42. J. D. Barrow and J. Stein-Schabes, Phys. Rev. D 32, 1595 (1985).
43. J. D. Barrow and F. J. Tipler, Phys. Rep. 56, 371 (1979).
44. M. V. Battisti and G. Montani, Phys. Lett. B 637, 203 (2006), arXiv:gr-qc/0604049.
45. M. V. Battisti and G. Montani, Phys. Lett. B 656, 96 (2007), arXiv:gr-qc/0703025.
46. M. V. Battisti and G. Montani, Phys. Rev. D 77, 023518 (2008), arXiv:0707.2726.
47. A. Beesham, Astrophys. Space Sci. 203, 169 (1993).
48. V. Belinskii and M. Francaviglia, Gen. Relativ. Gravit. 16, 1189 (1984).
49. V. A. Belinskii, Chaos in cosmology, in The Chaotic Universe, eds. V. G. Gurzadyan and R. Ruffini (World Scientific, Singapore, 2000), p. 350.
50. V. A. Belinskii and I. M. Khalatnikov, Sov. Phys. JETP 29, 911 (1969).
51. V. A. Belinskii and I. M. Khalatnikov, Sov. Phys. JETP 32, 169 (1971).
52. V. A. Belinskii and I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. 63, 1121 (1972).
53. V. A. Belinskii and I. M. Khalatnikov, Sov. Phys. JETP 36, 591 (1973).
54. V. A. Belinskii, I. M. Khalatnikov and E. M. Lifshitz, Adv. Phys. 19, 525 (1970).
55. V. A. Belinskii, I. M. Khalatnikov and E. M. Lifshitz, Sov. Phys. JETP 33, 1061 (1971).
56. V. A. Belinskii, I. M. Khalatnikov and E. M. Lifshitz, Sov. Phys. JETP 35, 838 (1972).
57. V. A. Belinskii, I. M. Khalatnikov and E. M. Lifshitz, Adv. Phys. 31, 639 (1982).
58. V. A. Belinskij and M. Francaviglia, Gen. Relativ. Gravit. 14, 213 (1982).
59. R. Benini, A. A. Kirillov and G. Montani, Class. Quantum Grav. 22, 1483 (2005), arXiv:gr-qc/0505027.
60. R. Benini and G. Montani, Phys. Rev. D 70, 103527 (2004), arXiv:gr-qc/0411044.
61. R. Benini and G. Montani, Class. Quantum Grav. 24, 387 (2007), arXiv:grqc/0612095.
62. R. Bergamini, P. Sedici and P. Verrocchio, Phys. Rev. D 55, 1896 (1997), arXiv:grqc/9612001.
63. B. K. Berger, Phys. Rev. D 39, 2426 (1989).
64. B. K. Berger, Gen. Relativ. Gravit. 7, 203 (1990).
65. B. K. Berger, Gen. Relativ. Gravit. 23, 1385 (1991).
66. B. K. Berger, Phys. Rev. D 47, 3222 (1993).
67. B. K. Berger, Phys. Rev. D 49, 1120 (1994), arXiv:gr-qc/9308016.
68. B. K. Berger, Class. Quantum Grav. 13, 1273 (1996), arXiv:gr-qc/9512005.
69. B. K. Berger, Phys. Rev. D 61, 023508 (1999), arXiv:gr-qc/9907083.
70. B. K. Berger, Approach to the singularity in spatially inhomogeneous cosmologies, arXiv:gr-qc/0106009.
71. B. K. Berger, Living Rev. Rel. 5, 1 (2002), http://www.livingreviews.org/lrr-2002-1, arXiv:gr-qc/0201056.
72. B. K. Berger, Class. Quantum Grav. 21, 81 (2004), arXiv:gr-qc/0312095.
73. B. K. Berger, D. Garfinkle, J. Isenberg, V. Moncrief and M. Weaver, Mod. Phys. Lett. A 13, 1565 (1998), arXiv:gr-qc/9805063.
74. B. K. Berger, D. Garfinkle and E. Strasser, Class. Quantum Grav. 14, L29 (1997), arXiv:gr-qc/9609072.
75. B. K. Berger and V. Moncrief, Phys. Rev. D 48, 4676 (1993), arXiv:gr-qc/9307032.
76. B. K. Berger and V. Moncrief, Phys. Rev. D 62, 023509 (2000), arXiv:gr-qc/0001083.
77. B. K. Berger and V. Moncrief, Phys. Rev. D 62, 123501 (2000), arXiv:gr-qc/0006071.
78. A. L. Berkin, Phys. Rev. D 46, 1551 (1992).
79. D. Bernard, Phys. Rev. D 33, 3581 (1986).
80. L. Bianchi, Sugli spazi a tre dimensioni che ammettono un gruppo continuo di movimenti, Opere, Vol. 9 (Edizione Cremonese, Roma, 1897)
81. [R. Jantzen, Gen. Relativ. Gravit. 33, 2171 (2001)].
82. L. Bianchi, Mem. Mat. Fis. Soc. Ital. Sci. 11, 267 (1898).
83. M. Biesiada, Class. Quantum Grav. 12, 715 (1995).
84. M. Biesiada and M. Szydłowski, Phys. Lett. A 160, 123 (1991).
85. S. Bleher, C. Grebogi, E. Ott and R. Brown, Phys. Rev. A 38, 930 (1988).
86. S. Bleher, E. Ott and C. Grebogi, Phys. Rev. Lett. 63, 919 (1989).
87. W. F. Blyth and C. J. Isham, Phys. Rev. D 11, 768 (1975).
88. O. Bogoyavlenskii and S. Novikov, Sov. Phys. JETP 37, 747 (1973).
89. M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001), arXiv:gr-qc/0102069.
90. M. Bojowald, Phys. Rev. Lett. 89, 261301 (2002), arXiv:gr-qc/0206054.
91. M. Bojowald, Class. Quantum Grav. 19, 2717 (2002), arXiv:gr-qc/0202077.
92. M. Bojowald, Gen. Relativ. Gravit. 38, 1771 (2006), arXiv:gr-qc/0609034.
93. M. Bojowald, AIP Conf. Proc. 910, 294 (2007), arXiv:gr-qc/0702144.
94. M. Bojowald and G. Date, Phys. Rev. Lett. 92, 071302 (2004), arXiv:gr-qc/0311003.
95. M. Bojowald, G. Date and G. Mortuza Hossain, Class. Quantum Grav. 21, 3541 (2004), arXiv:gr-qc/0404039.
96. M. Bojowald, G. Date and K. Vandersloot, Class. Quantum Grav. 21, 1253 (2004), arXiv:gr-qc/0311004.
97. B. Bolen, L. Bombelli and A. Corichi, Class. Quantum Grav. 21, 4087 (2004), arXiv:gr-qc/0404004.
98. J. M. Bradley and E. Sviestins, Gen. Relativ. Gravit. 16, 1119 (1984).
99. M. Bridges, J. D. McEwen, A. N. Lasenby and M. P. Hobson, Mon. Not. R. Astron. Soc. 377, 1473 (2007), arXiv:astro-ph/0605325.
100. J. D. Brown and K. V. Kuchař, Phys. Rev. D 51, 5600 (1995), arXiv:grqc/9409001.
101. J. Brunnemann and T. Thiemann, Class. Quantum Grav. 23, 1395 (2006), arXiv:grqc/0505032.
102. M. H. Bugalho, A. Rica da Silva and J. Sousa Ramos, Gen. Relativ. Gravit. 18, 1263 (1986).
103. A. Burd and R. Tavakol, Phys. Rev. D 47, 5336 (1993).
104. A. B. Burd, N. Buric and G. F. R. Ellis, Gen. Relativ. Gravit. 22, 349 (1990).
105. A. B. Burd, N. Buric and R. K. Tavakol, Class. Quantum Grav. 8, 123 (1991).
106. N. Caderni and R. Fabbri, Phys. Lett. A 67, 19 (1978).
107. S. Capozziello, G. Marmo, C. Rubano and P. Scudellaro, Int. J. Mod. Phys. D 6, 491 (1997), arXiv:gr-qc/9606050.
108. M. Carmeli and C. Charach, Phys. Lett. A 75, 333 (1980).
109. M. Carmeli, C. Charach and A. Feinstein, Ann. Phys. 150, 392 (1983).
110. D. Cartin and G. Khanna, Phys. Rev. Lett. 94, 111302 (2005), arXiv:gr-qc/0501016.
111. D. Cartin and G. Khanna, Phys. Rev. D 72, 084008 (2005), arXiv:gr-qc/0506024.
112. M. Castagnino and F. D. Mazzitelli, Phys. Rev. D 31, 742 (1985).
113. L. Cayón, A. J. Banday, T. Jaffe, H. K. Eriksen, F. K. Hansen, K. M. Gorski and J. Jin, Mon. Not. R. Astron. Soc. 369, 598 (2006), arXiv:astro-ph/0602023.
114. J. L. Cervantes-Cota and P. A. Chauvet, Phys. Rev. D 59, 043501 (1999), arXiv:grqc/9810064.
115. J. L. Cervantes-Cota and M. Nahmad, Gen. Relativ. Gravit. 33, 767 (2001), arXiv:grqc/0005032.
116. S. Chakraborty and G. C. Nandy, Int. J. Mod. Phys. D 5, 65 (1996).
117. S. Chakraborty and B. C. Paul, Phys. Rev. D 64, 127502 (2001).
118. S. Chakraborty and A. Roy, Astrophys. Space Sci. 253, 205 (1997).
119. N. Chakravarty and L. Biswas, Astrophys. Space Sci. 312, 329 (2007).
120. S. Chakravarty and M. J. Ablowitz, Phys. Rev. Lett. 76, 857 (1996).
121. C. Charach, Phys. Rev. D 26, 3367 (1982).
122. P. Chauvet, J. Cervantes-Cota and H. N. Núñez-Yépez, Class. Quantum Grav. 9, 1923 (1992).
123. C.-M. Chen, T. Harko and M. K. Mak, Phys. Rev. D 62, 124016 (2000), arXiv:hepth/0004096.
124. D. F. Chernoff and J. D. Barrow, Phys. Rev. Lett. 50, 134 (1983).
125. C. Cherubini, D. Bini, M. Bruni and Z. Perjes, Class. Quantum Grav. 22, 1763 (2005), arXiv:gr-qc/0408040.
126. T. Chiba, S. Mukohyama and T. Nakamura, Phys. Lett. B 408, 47 (1997), arXiv:grqc/9707043.
127. L. P. Chimento and M. S. Mollerach, Phys. Lett. A 121, 7 (1987).
128. D.-W. Chiou, Phys. Rev. D 75, 024029 (2007), arXiv:gr-qc/0609029.
129. D.-W. Chiou and K. Vandersloot, Phys. Rev. D 76, 084015 (2007), arXiv:0707.2548.
130. D. M. Chitre, Phys. Rev. D 6, 3390 (1972).
131. D. M. Chitre, Investigation of vanishing of a horizon for Bianchi type IX (the Mixmaster universe), PhD thesis, University of Maryland (1972), Technical Report No. 72-125.
132. P. Chmielowski and D. N. Page, Phys. Rev. D 38, 2392 (1988).
133. H. T. Cho and A. D. Speliotopoulos, Phys. Rev. D 52, 5445 (1995), arXiv:grqc/9504046.
134. F. Christiansen, H. H. Rugh and S. E. Rugh, J. Phys. A: Math. Gen. 28, 657 (1995).
135. T. Christodoulakis, T. Gakis and G. O. Papadopoulos, Class. Quantum Grav. 19, 1013 (2002), arXiv:gr-qc/0106065.
136. T. Christodoulakis, T. Grammenos, C. Helias, P. G. Kevrekidis and A. Spanou, J. Math. Phys. 47, 2505 (2006), arXiv:gr-qc/0506132.
137. T. Christodoulakis, E. Korfiatis and G. O. Papadopoulos, Commun. Math. Phys. 226, 377 (2002), arXiv:gr-qc/0107050.
138. T. Christodoulakis and G. O. Papadopoulos, Phys. Lett. B 501, 264 (2001), arXiv:grqc/0009074.
139. S. Coleman, Nucl. Phys. B 310, 643 (1988).
140. S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
141. A. Coley, Class. Quantum Grav. 19, L45 (2002), arXiv:hep-th/0110117.
142. A. A. Coley and S. Hervik, Class. Quantum Grav. 21, 4193 (2004), arXiv:grqc/0406120.
143. A. A. Coley and J. Wainwright, Class. Quantum Grav. 9, 651 (1992).
144. C. B. Collins and G. F. R. Ellis, Phys. Rep. 56, 65 (1979).
145. C. B. Collins and S. W. Hawking, Mon. Not. R. Astron. Soc. 162, 307 (1973).
146. C. B. Collins and S. W. Hawking, Astrophys. J. 180, 317 (1973).
147. G. Contopoulos, B. Grammaticos and A. Ramani, J. Phys. A: Math. Gen. 26, 5795 (1993).
148. G. Contopoulos, B. Grammaticos and A. Ramani, in Deterministic Chaos in General Relativity, eds. D. Hobill, D. Bernstein, D. Simpkins and M. Welge (Plenum Press, 1994), p. 423.
149. G. Contopoulos, B. Grammaticos and A. Ramani, J. Phys. A: Math. Gen. 27, 5357 (1994).
150. I. P. Cornfeld, S. V. Fomin and I. A. G. Sinai, Ergodic Theory (Springer, Berlin, 1982).
151. N. J. Cornish and J. J. Levin, Phys. Rev. D 55, 7489 (1997), arXiv:gr-qc/9612066.
152. N. J. Cornish and J. J. Levin, Phys. Rev. Lett. 78, 998 (1997), arXiv:gr-qc/9605029.
153. N. J. Cornish and J. J. Levin, The Mixmaster universe is unambiguously chaotic, in Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, eds. T. Piran and R. Ruffini (World Scientific, 1999), p. 616.
154. G. Corvino and G. Montani, Mod. Phys. Lett. A 19, 2777 (2004), arXiv:grqc/0410026.
155. S. Cotsakis and P. G. L. Leach, J. Phys. A: Math. Gen. 27, 1625 (1994).
156. S. Cotsakis, R. L. Lemmer and P. G. L. Leach, Phys. Rev. D 57, 4691 (1998), arXiv:gr-qc/9712027.
157. O. Coussaert and M. Henneaux, Class. Quantum Grav. 10, 1607 (1993), arXiv:grqc/9301001.
158. A. Csordás, R. Graham and P. Szépfalusy, Phys. Rev. A 44, 1491 (1991).
159. R. Cushman and J. Sniatycki, Rep. Math. Phys. 36, 75 (1995).
160. T. Damour and M. Henneaux, Phys. Rev. Lett. 85, 920 (2000), arXiv:hepth/0003139.
161. T. Damour and M. Henneaux, Phys. Lett. B 488, 108 (2000), arXiv:hepth/0006171.
162. T. Damour and M. Henneaux, Phys. Rev. Lett. 86, 4749 (2001), arXiv:hepth/0012172.
163. T. Damour, M. Henneaux, B. Julia and H. Nicolai, Phys. Lett. B 509, 323 (2001), arXiv:hep-th/0103094.
164. T. Damour, M. Henneaux and H. Nicolai, Class. Quantum Grav. 20, 020 (2003), arXiv:hep-th/0212256.
165. G. Date, Phys. Rev. D 72, 067301 (2005), arXiv:gr-qc/0505030.
166. P. de Bernardis, Nature 404, 955 (2000), arXiv:astro-ph/0004404.
167. A. de Moura and C. Grebogi, Phys. Rev. Lett. 86, 2778 (2001).
168. A. de Moura and C. Grebogi, Phys. Rev. E 66, 046214 (2002).
169. H. P. de Oliveira, A. M. O. de Almeida, I. D. Soares and E. V. Tonini, Phys. Rev. D 65, 083511 (2002), arXiv:gr-qc/0202047.
170. P. D. D'Eath, S. W. Hawking and O. Obergón, Phys. Lett. B 300, 44 (1993).
171. J. Demaret and Y. de Rop, Phys. Lett. B 299, 223 (1993).
172. J. Demaret, J. L. Hanquin, M. Henneaux and P. Spindel, Nucl. Phys. B 252, 538 (1985).
173. J. Demaret, J. L. Hanquin, M. Henneaux, P. Spindel and A. Taormina, Phys. Lett. B 175, 129 (1986).
174. J. Demaret, M. Henneaux and P. Spindel, Phys. Lett. B 164, 27 (1985).
175. J. Demaret and C. Scheen, J. Phys. A: Math. Gen. 29, 59 (1996).
176. M. Demianski, M. Heller and M. Szydlowski, Phys. Rev. D 36, 2945 (1987).
177. B. S. DeWitt, Phys. Rev. 160, 1113 (1967).
178. B. S. DeWitt, Phys. Rev. 162, 1195 (1967).
179. B. S. DeWitt, Phys. Rev. 162, 1239 (1967).
180. L. di Menza and T. Lehner, Gen. Relativ. Gravit. 36, 2635 (2004).
181. P. Dirac, Lectures on Quantum Mechanics, Belfer Graduate of Science (Yeshiva University, New York, 1964).
182. A. G. Doroshkevich, V. N. Lukash and I. D. Novikov, Zh. Eksp. Teor. Fiz. 60, 1201 (1971).
183. A. G. Doroshkevich and I. D. Novikov, Sov. Astron. 14, 763 (1971).
184. G. F. R. Ellis, Gen. Relativ. Gravit. 38, 1003 (2006).
185. G. F. R. Ellis and M. A. H. MacCallum, Commun. Math. Phys. 12, 108 (1969).
186. Y. Elskens, Phys. Rev. D 28, 1033 (1983).
187. Y. Elskens, J. Stat. Phys. 48, 1269 (1987).
188. Y. Elskens and M. Henneaux, Nucl. Phys. B 290, 111 (1987).
189. J. K. Erickson, D. H. Wesley, P. J. Steinhardt and N. Turok, Phys. Rev. D 69, 063514 (2004), arXiv:hep-th/0312009.
190. G. Esposito, Quantum Gravity, Quantum Cosmology and Lorentzian Geometries, Lecture Notes in Physics, Vol. M12 (Springer-Verlag, Berlin, 1994).
191. R. Fabbri and M. Tamburrano, Astron. Astrophys. 179, 11 (1987).
192. S. Fay, Gen. Relativ. Gravit. 21, 1609 (2004), arXiv:gr-qc/0402104.
193. S. Fay, Gen. Relativ. Gravit. 37, 1233 (2005), arXiv:gr-qc/0509070.
194. S. Fay and T. Lehner, Gen. Relativ. Gravit. 37, 1097 (2005), arXiv:grqc/0509071.
195. G. J. Fee, Homogeneous spacetimes, Master's thesis (1979).
196. K. Ferraz and G. Francisco, Phys. Rev. D 45, 1158 (1992).
197. K. Ferraz, G. Francisco and G. E. A. Matsas, Mixmaster: A weakly chaotic model?, NASA STI/Recon Tech. Rep. N 92, 15945 (1990).
198. K. Ferraz, G. Francisco and G. E. A. Matsas, Phys. Lett. A 156, 407 (1991).
199. A. E. Fischer and J. E. Marsden, J. Math. Phys. 13, 546 (1972).
200. K. Fišer, K. Rosquist and C. Uggla, Gen. Relativ. Gravit. 24, 679 (1992).
201. V. N. Folomeev and V. T. Gurovich, Gen. Relativ. Gravit. 32, 1255 (2000), arXiv:grqc/0001065.
202. V. N. Folomeev and V. T. Gurovich, Grav. Cosmol. 6, 19 (2000).
203. G. Francisco and G. E. A. Matsas, Gen. Relativ. Gravit. 20, 1047 (1988).
204. Y. Furihata and K. Sato, Class. Quantum Grav. 10, 1147 (1993).
205. T. Furusawa, Prog. Theor. Phys. 75, 59 (1986).
206. T. Furusawa, Prog. Theor. Phys. 76, 67 (1986).
207. R. García-Salcedo and N. Bretón, Class. Quantum Grav. 20, 5425 (2003), arXiv:hepth/0212130.
208. R. Geroch, E. H. Kronheimer and R. Penrose, R. Soc. London Proc., Ser. A 327, 545 (1972).
209. R. Geroch, C. B. Liang and R. M. Wald, J. Math. Phys. 23, 432 (1982).
210. E. Giannetto and P. Salucci, Phys. Lett. B 152, 171 (1985).
211. K. Giesel and T. Thiemann, Class. Quantum Grav. 24, 2465 (2007), arXiv:grqc/0607099.
212. K. Giesel and T. Thiemann, Class. Quantum Grav. 24, 2499 (2007), arXiv:grqc/0607100.
213. K. Giesel and T. Thiemann, Class. Quantum Grav. 24, 2565 (2007), arXiv:grqc/0607101.
214. D. Giulini and D. Marolf, Class. Quantum Grav. 16, 2479 (1999), arXiv:grqc/9812024.
215. S. A. Gogilidze, A. M. Khvedelidze, D. M. Mladenov and V. N. Perbuhin, Grav. Cosmol. 3, 85 (1997).
216. G. González and R. S. Tate, Class. Quantum Grav. 12, 1287 (1995), arXiv:grqc/9412015.
217. M. J. Gotay and J. Demaret, Phys. Rev. D 28, 2402 (1983).
218. R. Graham, Phys. Rev. Lett. 67, 1381 (1991).
219. R. Graham, Chaos Soliton Fract. 5, 1103 (1995), arXiv:gr-qc/9403030.
220. R. Graham, R. Hübner, P. Szépfalusy and G. Vattay, Phys. Rev. A 44, 7002 (1991).
221. R. Graham and H. Luckock, Phys. Rev. D 49, R4981 (1994).
222. R. Graham and R. Paternoga, Phys. Rev. D 54, 2589 (1996), arXiv:gr-qc/9603027.
223. R. Graham and P. Szépfalusy, Phys. Rev. D 42, 2483 (1990).
224. C. Grebogi, E. Ott, S. Pelikan and J. Yorke, Physica D 13, 261 (1984).
225. L. P. Grishchuk, A. G. Doroshkevich and V. M. Yudin, Zh. Eksp. Teor. Fiz. 69, 1857 (1975).
226. Ø. Grøn, Phys. Rev. D 33, 1204 (1986).
227. D. J. Gross and P. F. Mende, Nucl. Phys. B 303, 407 (1988).
228. B. Grubišić and V. Moncrief, Phys. Rev. D 47, 2371 (1993), arXiv:gr-qc/9209006.
229. B. Grubišić and V. Moncrief, Phys. Rev. D 49, 2792 (1994), arXiv:gr-qc/9309007.
230. A. H. Guth, Phys. Rev. D 23, 347 (1981).
231. A. H. Guth and S. Pi, Phys. Rev. Lett. 49, 1110 (1982).
232. E. Guzman, Astrophys. Space Sci. 199, 289 (1993).
233. E. Guzman, Int. J. Theor. Phys. 35, 419 (1996).
234. R. Haag, Local Quantum Physics (Springer, New York, 1992).
235. J. J. Halliwell, Phys. Rev. D 43, 2590 (1991).
236. P. Halpern, Gen. Relativ. Gravit. 19, 73 (1987).
237. P. Halpern, Phys. Rev. D 66, 027503 (2002), arXiv:gr-qc/0203055.
238. P. Halpern, Gen. Relativ. Gravit. 35, 251 (2003), arXiv:gr-qc/0207056.
239. N. W. Halverson, Dasi first results: A measurement of the cosmic microwave background angular power spectrum, Technical Report, arXiv:astro-ph/0104489.
240. M. Han and Y. Ma, Phys. Lett. B 635, 225 (2006), arXiv:gr-qc/0510014.
241. J. L. Hanquin and J. Demaret, Class. Quantum Grav. 1, 291 (1984).
242. C. O. Hans and R. Ruffini, Gravitation and Spacetime (WW Norton, New York, 1994).
243. T. Harko and M. K. Mak, Class. Quantum Grav. 21, 1489 (2004), arXiv:grqc/0401069.
244. J. B. Hartle, in Highlights in Gravitation and Cosmology, eds. A. K. B. Iyer, J. V. Narlikar and C. Vishveshuara (Cambridge University Press, Cambridge, 1988).
245. J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2960 (1983).
246. S. Hawking, Mon. Not. R. Astron. Soc. 142, 129 (1969).
247. S. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, 1973).
248. J. F. Heagy and S. M. Hammel, Physica D 70, 140 (1994).
249. J. M. Heinzle and C. Uggla, Class. Quantum Grav. 23, 3463 (2006), arXiv:grqc/0512031.
250. J. M. Heinzle, C. Uggla and N. Rohr, The cosmological billiard attractor, arXiv:grqc/0702141.
251. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, 1992).
252. A. B. Henriques, J. M. Mourão and P. M. Sá, Phys. Lett. B 256, 359 (1991).
253. S. Hervik, Class. Quantum Grav. 17, 2765 (2000), arXiv:gr-qc/0003084.
254. C. G. Hewitt, R. Bridson and J. Wainwright, Gen. Relativ. Gravit. 33, 65 (2001), arXiv:gr-qc/0008037.
255. C. G. Hewitt and J. Wainwright, Class. Quantum Grav. 10, 99 (1993).
256. D. Hobill, New York Acad. Sci. Ann. 631, 15 (1991).
257. D. Hobill, D. Bernstein, M. Welge and D. Simkins, Class. Quantum Grav. 8, 1155 (1991).
258. D. Hobill, A. Burd and A. Coley, Deterministic Chaos in General Relativity (Plenum Press, New York, 1994).
259. P. Horava, Class. Quantum Grav. 8, 2069 (1991).
260. J. T. Horwood and J. Wainwright, Gen. Relativ. Gravit. 36, 799 (2004), arXiv:grqc/0309083.
261. A. Hosoya, L. G. Jensen and J. A. Stein-Schabes, Nucl. Phys. B 283, 657 (1987).
262. B. L. Hu, Phys. Rev. D 8, 1048 (1973).
263. B. L. Hu, Phys. Rev. D 9, 3263 (1974).
264. B. L. Hu, Phys. Rev. D 12, 1551 (1975).
265. B. L. Hu, Phys. Rev. D 18, 969 (1978).
266. B. L. Hu and D. J. O'Connor, Phys. Rev. D 34, 2535 (1986).
267. B. L. Hu and T. Regge, Phys. Rev. Lett. 29, 1616 (1972).
268. K. Huang, Statistical Mechanics (Wiley, New York, 1987).
269. W. Huang, Phys. Rev. D 58, 084007 (1998), arXiv:hep-th/0209092.
270. W.-H. Huang, Phys. Lett. A 129, 429 (1988).
271. J. Ibáñez, R. J. van den Hoogen and A. A. Coley, Phys. Rev. D 51, 928 (1995).
272. G. P. Imponente and G. Montani, Int. J. Mod. Phys. D 11, 1321 (2001), arXiv:grqc/0106028.
273. G. P. Imponente and G. Montani, Phys. Rev. D 63, 103501 (2001), arXiv:astroph/0102067.
274. G. P. Imponente and G. Montani, Nucl. Phys. B (Proc. Suppl.) 104, 193 (2002), arXiv:gr-qc/0111051.
275. G. P. Imponente and G. Montani, Int. J. Mod. Phys. D 12, 977 (2003), arXiv:grqc/0404106.
276. G. P. Imponente and G. Montani, J. Korean Phys. Soc. 42, S54 (2003), arXiv:grqc/0201102.
277. G. P. Imponente and G. Montani, Int. J. Mod. Phys. D 12, 1845 (2003), arXiv:grqc/0307048.
278. G. P. Imponente and G. Montani, Physica A 338, 282 (2004), arXiv:gr-qc/0401086.
279. J. Isenberg and V. Moncrief, Ann. Phys. 199, 84 (1990), arXiv:gr-qc/9209006.
280. C. J. Isham, Canonical quantum gravity and the problem of time, arXiv:grqc/9210011.
281. V. D. Ivashchuk, V. N. Mel'Nikov and A. A. Kirillov, Sov. J. Exp. Theor. Phys. Lett. 60, 235 (1994).
282. T. R. Jaffe, A. J. Banday, H. K. Eriksen, K. M. Górski and F. K. Hansen, Astron. Astrophys. 460, 393 (2006), arXiv:astro-ph/ 0606046.
283. T. R. Jaffe, S. Hervik, A. J. Banday and K. M. Górski, Astrophys. J. 644, 701 (2006), arXiv:astro-ph/0512433.
284. Y. Jin and K.-I. Maeda, Phys. Rev. D 71, 064007 (2005), arXiv:gr-qc/0412060.
285. R. A. Johnson, J. Math. Phys. 18, 898 (1977).
286. M. Joy and V. C. Kuriakose, Phys. Rev. D 62, 104017 (2000), arXiv:hep-th/0008234.
287. T. W. Judson, Abstract Algebra: Theory and Applications (PWS, 1994).
288. W. Kao, Phys. Rev. D 64, 107301 (2001), arXiv:hep-th/0104166.
289. E. Kasner, Adv. Phys. 43, 217 (1921).
290. A. Kempf and G. Mangano, Phys. Rev. D 55, 7909 (1997), arXiv:hep-th/9612084.
291. A. Kempf, G. Mangano and R. B. Mann, Phys. Rev. D 52, 1108 (1995), arXiv:hepth/9412167.
292. I. M. Khalatnikov, A. Y. Kamenshchik, M. Martellini and A. A. Starobinsky, J. Cosmol. Astropart. Phys. 03003, 001 (2003), arXiv:gr-qc/0301119.
293. I. M. Khalatnikov, A. Y. Kamenshchik and A. A. Starobinsky, Class. Quantum Grav. 19, 3845 (2002), arXiv:gr-qc/0204045.
294. I. M. Khalatnikov and E. M. Lifshitz, Adv. Phys. 12, 185 (1963).
295. I. M. Khalatnikov et al., Pis'ma Zh. Eksp. Teor. Fiz. 38, 79 (1983)
296. [JETP Lett. 38, 91 (1983)].
297. I. M. Khalatnikov et al., J. Stat. Phys. 38, 97 (1985).
298. A. Kheyfets, W. A. Miller and R. Vaulin, Class. Quantum Grav. 23, 4333 (2006), arXiv:gr-qc/0512040.
299. J. Kijowski and G. Magli, Class. Quantum Grav. 15, 3891 (1998), arXiv:grqc/9709021.
300. A. A. Kirillov, JETP Lett. 55, 561 (1992).
301. A. A. Kirillov, Sov. Phys. JETP 76, 355 (1993).
302. A. A. Kirillov, Grav. Cosmol., Suppl. 4, 23 (1998).
303. A. A. Kirillov and A. A. Kochnev, Pis'ma Zh. Eksp. Teor. Fiz. 46, 345 (1987).
304. A. A. Kirillov and V. N. Melnikov, Phys. Rev. D 52, 723 (1995), arXiv:gr-qc/9408004.
305. A. A. Kirillov and G. Montani, Phys. Rev. D 56, 6225 (1997).
306. A. A. Kirillov and G. Montani, JETP Lett. 66, 475 (1997).
307. A. A. Kirillov and G. Montani, Phys. Rev. D 66, 064010 (2002), arXiv:gr-qc/0209054.
308. Y. Kitada and K. Maeda, Class. Quantum Grav. 10, 703 (1993).
309. H. Kodama, Prog. Theor. Phys. 80, 1024 (1988).
310. H. Kodama, Prog. Theor. Phys. 107, 305 (2002), arXiv:gr-qc/0109064.
311. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Reading, New York, 1990).
312. A. Krasiński, C. G. Behr, E. Schücking, F. B. Estabrook, H. D. Wahlquist, G. F. R. Ellis, R. Jantzen and W. Kundt, Gen. Relativ. Gravit. 35, 475 (2003).
313. K. D. Krori and M. Barua, Phys. Lett. A 123, 379 (1987).
314. K. D. Krori, K. Pathak and S. Dutta, Gen. Relativ. Gravit. 31, 1423 (1999).
315. K. Kuchař, J. Math. Phys. 13, 768 (1972).
316. K. Kuchař, Canonical methods of quantization, in Quantum Gravity II, eds. C. J. Isham, R. Penrose and D. W. Sciama (Clarendon Press, 1981), p. 329.
317. K. Kuchař and C. Torre, Phys. Rev. D 43, 419 (1991).
318. K. V. Kuchař and M. P. Ryan, Phys. Rev. D 40, 3982 (1989).
319. L. D. Landau and E. M. Lifshitz, Relativistic Quantum Mechanics (Pergamon Press, Elmsford, New York, 1973).
320. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields, 4th edn. (Addison-Wesley, New York, 1975).
321. A. Latifi, M. Musette and R. Conte, Physica D 87, 70 (1995).
322. V. G. Leblanc, Class. Quantum Grav. 14, 2281 (1997).
323. V. G. Leblanc, Class. Quantum Grav. 15, 1607 (1998).
324. A. T. Lee, et al., Astrophys. J. 561, L1 (2001), arXiv:astro-ph/0104459.
325. J. Lewandowski, A. Okolow, H. Sahlmann and T. Thiemann, Commun. Math. Phys. 267, 703 (2006), arXiv:gr-qc/0504147.
326. E. M. Lifshitz and I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. 39, 149 (1960).
327. E. M. Lifshitz, I. M. Lifshitz and I. M. Khalatnikov, Sov. Phys. JETP 32, 173 (1971).
328. A. D. Linde, Phys. Lett. B 129, 177 (1983).
329. E. R. Livine, Towards a covariant loop quantum gravity, arXiv:gr-qc/0608135.
330. D. Lorenz-Petzold, Phys. Lett. A 79, 19 (1980).
331. D. Lorenz-Petzold, Phys. Lett. B 148, 43 (1984).
332. D. Lorenz-Petzold, Phys. Lett. B 149, 79 (1984).
333. D. Lorenz-Petzold, Phys. Lett. B 151, 105 (1985).
334. D. Lorenz-Petzold, Class. Quantum Grav. 2, 829 (1985).
335. D. Lorenz-Petzold, Phys. Rev. D 31, 929 (1985).
336. D. Lorenz-Petzold, Phys. Lett. B 153, 134 (1985).
337. D. Lorenz-Petzold, J. Astrophys. Astron. 6, 137 (1985).
338. D. Lorenz-Petzold, Phys. Lett. B 167, 157 (1986).
339. D. Lorenz-Petzold, J. Math. Phys. 28, 1382 (1987).
340. J. Louko, Phys. Rev. D 35, 3760 (1987).
341. H. Lü and C. N. Pope, Nucl. Phys. B 465, 127 (1996), arXiv:hep-th/9512012.
342. V. N. Lukash, Sov. Phys. JETP 40, 792 (1974).
343. J. P. Luminet, J. R. Weeks, A. Riazuelo, R. Lehoucq and J. P. Uzan, Nature 425, 593 (2003), arXiv:astro-ph/0310253.
344. A. M. Lyapunov, Comm. Soc. Math., Kharkov (1893)
345. [Ann. Fac. Sci. Toulouse 9, 203 (1907);
346. reprinted in Ann. Math. Stud. 17 (1949)].
347. R. Maartens, Living Rev. Rel. 7, 7 (2004), arXiv:gr-qc/0312059.
348. R. Maartens and S. D. Maharaj, Gen. Relativ. Gravit. 22, 595 (1990).
349. R. Maartens and M. F. Wolfaardt, Class. Quantum Grav. 9, 1525 (1992).
350. M. A. H. MacCallum, Nature Phys. Sci. 230, 112 (1971).
351. M. A. H. MacCallum, Phys. Lett. A 40, 385 (1972).
352. M. A. H. MacCallum, Anisotropic and inhomogeneous relativistic cosmologies, in General Relativity: An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, 1979).
353. A. J. Maciejewski and M. Szydlowski, J. Phys. A: Math. Gen. 31, 2031 (1998), arXiv:gr-qc/9702045.
354. S. Major and L. Smolin, Mixmaster quantum cosmology in terms of physical dynamics, arXiv:gr-qc/9607020.
355. M. K. Mak, T. Harko and L. Z. Fang, Int. J. Mod. Phys. D 11, 447 (2002), arXiv:grqc/0110069.
356. J. Malecki, Phys. Rev. D 70, 084040 (2004), arXiv:gr-qc/0407114.
357. N. Manojlović and G. A. Mena Marugán, Phys. Rev. D 48, 3704 (1993), arXiv:grqc/9304041.
358. N. Manojlović and A. Miković, Class. Quantum Grav. 10, 559 (1993).
359. N. Manojlović and A. Miković, J. Math. Phys. 41, 4777 (2000), arXiv:mathph/0002037.
360. D. Marolf, Class. Quantum Grav. 12, 1441 (1995), arXiv:gr-qc/9409049.
361. A. Mazumder, Gen. Relat. Gravit. 26, 307 (1994).
362. J. D. McEwen, M. P. Hobson, A. N. Lasenby and D. J. Mortlock, Mon. Not. R. Astron. Soc. 369, 1858 (2006), arXiv:astro-ph/0510349.
363. C. B. G. McIntosh and J. D. Steele, Class. Quantum Grav. 8, 1173 (1991).
364. S. Mercuri and G. Montani, Mod. Phys. Lett. A 19, 1519 (2004), arXiv:grqc/0312077.
365. S. Mercuri and G. Montani, Int. J. Mod. Phys. D 13, 165 (2004), arXiv:grqc/0310077.
366. P. G. Miedema, Phys. Rev. D 50, 2431 (1994).
367. P. G. Miedema and W. A. van Leeuwen, Class. Quantum Grav. 9, 183 (1992).
368. P. G. Miedema and W. A. van Leeuwen, Phys. Rev. D 47, 3151 (1993).
369. E. Milaneschi and R. Fabbri, Astron. Astrophys. 151, 7 (1985).
370. C. W. Misner, Phys. Rev. Lett. 22, 1071 (1969).
371. C. W. Misner, Phys. Rev. 186, 1319 (1969).
372. C. W. Misner, The Mixmaster cosmological metrics, arXiv:gr-qc/9405068.
373. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, New York, 1973).
374. G. Mohanty and B. Mishra, Astrophys. Space Sci. 283, 67 (2003).
375. G. Mohanty, S. K. Sahu and P. K. Sahoo, Astrophys. Space Sci. 288, 523 (2003).
376. V. Moncrief and M. P. Ryan, Phys. Rev. D 44, 2375 (1991).
377. G. Montani, Class. Quantum Grav. 12, 2505 (1995).
378. G. Montani, Class. Quantum Grav. 16, 723 (1999).
379. G. Montani, in The Chaotic Universe, Advanced Series in Astrophysics and Cosmology, Vol. 10, eds. V. G. Gurzadyan and R. Ruffini (World Scientific, Singapore, 2000).
380. G. Montani, Class. Quantum Grav. 17, 2205 (2000).
381. G. Montani, Class. Quantum Grav. 17, 2197 (2000).
382. G. Montani, Nuovo Cimento B 116, 1375 (2001).
383. G. Montani, Nucl. Phys. B 634, 370 (2002), arXiv:gr-qc/0205032.
384. G. Montani, Int. J. Mod. Phys. D 12, 1445 (2003), arXiv:gr-qc/0307069.
385. G. Montani, Int. J. Mod. Phys. D 13, 1703 (2004), arXiv:gr-qc/0404105.
386. G. Montani, Int. J. Mod. Phys. D 13, 1029 (2004), arXiv:gr-qc/0404030.
387. J. Moser, E. Phillips and S. Varadhan, Dynamical System, Theory and Applications, Vol. 38 (Springer-Verlag, Berlin, 1975).
388. J. Moser, E. Phillips and S. Varadhan, Ergodic Theory (Courant Institute of Mathematical Sciences, New York University, New York, 1975).
389. A. E. Motter, Phys. Rev. Lett. 91, 231101 (2003), arXiv:gr-qc/0305020.
390. A. E. Motter and P. S. Letelier, Phys. Lett. A 285, 127 (2001), arXiv:gr-qc/0011001.
391. G. Mukherjee, J. Astrophys. Astron. 4, 295 (1983).
392. H. Nariai, Prog. Theor. Phys. 58, 842 (1977).
393. H. Nariai, Prog. Theor. Phys. 57, 67 (1977).
394. B. K. Nayak and B. K. Sahoo, Gen. Relativ. Gravit. 21, 211 (1989).
395. C. B. Netterfield et al., Astrophys. J. 571, 604 (2002), arXiv:astro-ph/0104460.
396. H. Nicolai, K. Peeters and M. Zamaklar, Class. Quantum Grav. 22, R193 (2005), arXiv:hep-th/0501114.
397. U. S. Nilsson and C. Uggla, J. Math. Phys. 38, 2611 (1997), arXiv:gr-qc/9702039.
398. U. S. Nilsson, C. Uggla and J. Wainwright, Gen. Relativ. Gravit. 32, 1319 (2000), arXiv:gr-qc/9908062.
399. U. S. Nilsson, C. Uggla and J. Wainwright, Gen. Relativ. Gravit. 32, 1981 (2000).
400. O. Obregón, J. Pullin and M. P. Ryan, Phys. Rev. D 48, 5642 (1993), arXiv:grqc/9308001.
401. O. Obregon and M. P. Ryan, Jr., J. Math. Phys. 22, 623 (1981).
402. O. Obregon and J. Socorro, Int. J. Theor. Phys. 35, 1381 (1996), arXiv:grqc/9506021.
403. D. Oriti, Rep. Prog. Phys. 64, 1489 (2001), arXiv:gr-qc/0106091.
404. C. Ortiz, E. Mena-Barboza, M. Sabido and J. Socorro, (Non)commutative isotropization in Bianchi I with barotropic perfect fluid and Λ cosmological, arXiv:grqc/0703101.
405. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
406. T. Padmanabhan, Gen. Relativ. Gravit. 14, 549 (1982).
407. E. Palm, Quarterly J. Mech. Appl. Math. 10, 500 (1957).
408. S. L. Parnovsky, Class. Quantum Grav. 7, 571 (1990).
409. A. C. Patra, M. N. Sinha Roy and D. Ray, Int. J. Theor. Phys. 28, 415 (1989).
410. R. Penrose, Phys. Rev. Lett. 14, 57 (1965).
411. A. Perez, Class. Quantum Grav. 20, R43 (2003), arXiv:gr-qc/0301113.
412. Y. B. Pesin, UMN (Russ. Math. Surv.) 32, 55 (1977).
413. G. Pianigiani and J. Yorke, Trans. Am. Math. Soc. 252, 351 (1979).
414. D. Podolsky, General asymptotic solutions of the Einstein equations and phase transitions in quantum gravity, arXiv:0704.0354.
415. J. M. Pons and L. C. Shepley, Phys. Rev. D 58, 024001 (1998), arXiv:gr-qc/9805030.
416. A. Pontzen and A. Challinor, Mon. Not. R. Astron. Soc. 380, 1387 (2007), arXiv:0706.2075.
417. A. Pradhan and P. Pandey, Astrophys. Space Sci. 301, 127 (2006).
418. A. Pradhan, S. K. Srivastav and M. K. Yadav, Astrophys. Space Sci. 298, 419 (2005), arXiv:gr-qc/0307039.
419. S. A. Pritomanov, Phys. Lett. A 107, 33 (1985).
420. C. Pryke et al., Astrophys. J. 568, 46 (2002), arXiv:astro-ph/0104490.
421. J. Pullin, Relativity and gravitation: Classical and quantum, in Proc. VIIth SILARG Symp., eds. J. C. D'Olivio et al. (World Scientific, 1991).
422. R. Puzio, Class. Quantum Grav. 11, 609 (1994).
423. S. Ram, J. Math. Phys. 29, 449 (1988).
424. S. Ram, J. Math. Phys. 30, 757 (1989).
425. D. R. K. Reddy and R. Venkateswarlu, Astrophys. Space Sci. 136, 17 (1987).
426. A. D. Rendall, J. Math. Phys. 37, 438 (1996), arXiv:gr-qc/9505017.
427. A. D. Rendall, Class. Quantum Grav. 14, 2341 (1997), arXiv:gr-qc/9703036.
428. H. Ringstrom, Ann. Henri Poincaré 2, 405 (2001), arXiv:gr-qc/0006035.
429. V. Romano and D. Pavón, Phys. Rev. D 47, 1396 (1993).
430. K. Rosquist, Class. Quantum Grav. 1, 81 (1984).
431. K. Rosquist, C. Uggla and R. T. Jantzen, Class. Quantum Grav. 7, 625 (1990).
432. K. Rosquist, C. Uggla and R. T. Jantzen, Class. Quantum Grav. 7, 611 (1990).
433. K. Rosquist, C. Uggla, H. von Zur-Múhlen and R. T. Jantzen, Geometrized field equations for Bianchi cosmology, in Proc. 12th Int. Conf. on General Relativity and Gravitation, 2-8 July 1989, Boulder, Colorado, USA (1989), p. 351.
434. T. Rothman and M. S. Madsen, Phys. Lett. B 159, 256 (1985).
435. C. Rovelli, Phys. Rev. D 43, 442 (1991).
436. C. Rovelli, Class. Quantum Grav. 8, 297 (1991).
437. C. Rovelli, Living Rev. Rel. 1, 1 (1998), arXiv:gr-qc/9710008.
438. C. Rovelli, Quantum Gravity (Cambridge University Press, 2004).
439. C. Rovelli and T. Thiemann, Phys. Rev. D 57, 1009 (1998), arXiv:gr-qc/9705059.
440. S. R. Roy and S. K. Banerjee, Class. Quantum Grav. 14, 2845 (1997).
441. S. R. Roy and S. Narain, Astrophys. Space Sci. 108, 195 (1985).
442. S. R. Roy, S. Narain and J. P. Singh, Astrophys. Space Sci. 128, 447 (1986).
443. S. R. Roy and A. Prasad, Astrophys. Space Sci. 181, 61 (1991).
444. S. R. Roy and A. Prasad, Ind. J. Pure Appl. Math. 26, 169 (1995).
445. V. A. Ruban, Astron. Zh. 59, 1044 (1982).
446. S. E. Rugh, Chaos in the Einstein equations-characterization and importance?, in Deterministic Chaos in General Relativity, eds. D. Hobill, A. Burd and A. Coley (Plenum, 1994), p. 359.
447. S. E. Rugh and B. J. T. Jones, Phys. Lett. A 147, 353 (1990).
448. M. P. Ryan, Jr. and S. M. Waller, On the Hamiltonian formulation of class B Bianchi cosmological models, arXiv:gr-qc/9709012.
449. M. P. Ryan and L. C. Shepley, Homogeneous Relativistic Cosmologies (Princeton University Press, 1975).
450. M. P. Ryan, Jr., Ann. Phys. 65, 506 (1971).
451. M. P. Ryan, Jr., Ann. Phys. 65, 541 (1971).
452. P. M. Sá and A. B. Henriques, Phys. Lett. B 287, 61 (1992).
453. P. M. Saffin, Phys. Lett. B 465, 101 (1999), arXiv:gr-qc/9906001.
454. A. Sagnotti and B. Zwiebach, Phys. Rev. D 24, 305 (1981).
455. B. Saha, Mod. Phys. Lett. A 20, 2127 (2005), arXiv:gr-qc/0409104.
456. B. Saha and V. Rikhvitsky, Physica D 219, 168 (2006), arXiv:gr-qc/0410056.
457. P. Salucci and R. Fabbri, Nuovo Cimento B 77, 62 (1983).
458. J. Samuel, Class. Quantum Grav. 17, L141 (2000), arXiv:gr-qc/0005095.
459. V. A. Savchenko, T. P. Shestakova and G. M. Vereshkov, Int. J. Mod. Phys. A 14, 4473 (1999), arXiv:gr-qc/9909047.
460. C. Scheen and J. Demaret, Phys. Lett. B 399, 207 (1997).
461. J. Schirmer, Class. Quantum Grav. 12, 1099 (1995), arXiv:gr-qc/9408008.
462. H.-J. Schmidt, Astron. Nachr. 303, 227 (1982).
463. J. H. M. M. Schmitt, Astron. Astrophys. 87, 236 (1980).
464. J. Schneider and Z. Neufeld, Phys. Rev. E 66, 066218 (2002).
465. J. Silk and M. S. Turner, Phys. Rev. D 35, 419 (1987).
466. J. K. Singh and S. Ram, Astrophys. Space Sci. 225, 57 (1995).
467. H. Sirousse-Zia, Gen. Relativ. Gravit. 14, 751 (1982).
468. R. J. Slagter, Astrophys. J. 268, 513 (1983).
469. R. J. Slagter, Astrophys. J. 286, 379 (1984).
470. L. Smolin, An invitation to loop quantum gravity, arXiv:gr-qc/0408048.
471. I. D. Soares and T. J. Stuchi, Phys. Rev. D 73, 069901 (2006) [Erratum: Phys. Rev. D 72, 083516 (2005)].
472. D. N. Spergel et al., Astrophys. J. Suppl. 148, 175 (2003), arXiv:astro-ph/0302209.
473. F. Stancu, Group Theory in Subnuclear Physics (Clarendon Press, Oxford, 1996).
474. A. A. Starobinsky, JETP Lett. 30, 682 (1979).
475. A. A. Starobinsky, Pis'ma Zh. Eksp. Teor. Fiz. 37, 55 (1983).
476. H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge University Press, UK, 2003).
477. M. Szydlowski, Phys. Lett. A 176, 22 (1993).
478. M. Szydlowski, Grav. Cosmol. 2, 92 (1996).
479. M. Szydlowski, Gen. Relativ. Gravit. 29, 185 (1997).
480. M. Szydlowski and M. Biesiada, Phys. Rev. D 44, 2369 (1991).
481. M. Szydlowski, M. Biesiada and J. Szczesny, Phys. Lett. B 195, 27 (1987).
482. M. Szydlowski and M. Heller, Acta Cosmologica 20, 17 (1994).
483. M. Szydlowski and A. Krawiec, Phys. Rev. D 47, 5323 (1993).
484. M. Szydlowski and A. Lapeta, Phys. Lett. A 148, 239 (1990).
485. M. Szydlowski and J. Szczesny, Phys. Rev. D 50, 819 (1994).
486. G. E. Tauber, Int. J. Theor. Phys. 18, 371 (1979).
487. A. Terras, Harmonic Analysis on Symmetric Spaces and Applications I (Springer-Verlag, New York, 1985).
488. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, 2007).
489. T. Thiemann, Lect. Notes Phys. 721, 185 (2007), arXiv:hep-th/0608210.
490. T. Thiemann, Class. Quantum Grav. 23, 2249 (2006), arXiv:gr-qc/0510011.
491. P. Tod and C. Lübbe, A global conformal extension theorem for perfect fluid Bianchi space-times, arXiv:0710.5723.
492. K. Tomita and N. Deruelle, Phys. Rev. D 50, 7216 (1994).
493. C. G. Tsagas and R. Maartens, Class. Quantum Grav. 17, 2215 (2000), arXiv:grqc/9912044.
494. P. Turkowski, Phys. Lett. B 207, 36 (1988).
495. C. Uggla, K. Rosquist and R. T. Jantzen, Phys. Rev. D 42, 404 (1990).
496. C. Uggla, H. van Elst, J. Wainwright and G. F. R. Ellis, Phys. Rev. D 68, 103502 (2003), arXiv:gr-qc/0304002.
497. C. Uggla and H. von Zur-Mühlen, Class. Quantum Grav. 7, 1365 (1990).
498. W. G. Unruh and R. M. Wald, Phys. Rev. D 40, 2598 (1989).
499. B. Vakili, N. Khosravi and H. R. Sepangi, Class. Quantum Grav. 24, 931 (2007), arXiv:gr-qc/0701075.
500. B. Vakili and H. R. Sepangi, Phys. Lett. B 651, 79 (2007), arXiv:0706.0273.
501. R. J. van den Hoogen, A. A. Coley and Y. He, Phys. Rev. D 68, 023502 (2003), arXiv:gr-qc/0212094.
502. R. J. van den Hoogen and I. Olasagasti, Phys. Rev. D 59, 107302 (1999).
503. W. A. van Leeuwen, P. G. Miedema and S. H. Wiersma, Gen. Relativ. Gravit. 21, 413 (1989).
504. A. Vilenkin, Phys. Rev. D 37, 888 (1988).
505. A. Vilenkin, Phys. Rev. D 39, 1116 (1989).
506. S. D. P. Vitenti and D. Müller, Phys. Rev. D 74, 063508 (2006), arXiv:gr-qc/0604127.
507. J. Wainwright, A. A. Coley, G. F. R. Ellis and M. Hancock, Class. Quantum Grav. 15, 331 (1998).
508. R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
509. M. Weaver, J. Isenberg and B. K. Berger, Phys. Rev. Lett. 80, 2984 (1998), arXiv:grqc/9712055.
510. E. Weber, J. Math. Phys. 28, 1658 (1987).
511. E. Witten, Phys. Today 50, 28 (1997).
512. M. Wojtkowski, Ergod. Theory Dyn. Syst. 5, 145 (1985).
513. L. Xuefeng and R. M. Wald, Phys. Rev. D 41, 2444 (1990).
514. H. Yamazaki and T. Hara, Prog. Theor. Phys. 106, 323 (2001).
515. J. Yokoyama and K.-I. Maeda, Phys. Rev. D 41, 1047 (1990).
516. J. W. J. York, Phys. Rev. Lett. 28, 1082 (1972).
517. A. Zardecki, Phys. Rev. D 28, 1235 (1983).
518. A. Zardecki, Phys. Rev. D 31, 718 (1985).
519. I. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics. Volume 2. The Structure and Evolution of the Universe, revised and enlarged edition (University of Chicago Press, Chicago, IL, 1983).
520. Y. B. Zel'Dovich, Sov. J. Exp. Theor. Phys. Lett. 11, 197 (1970).