Poincaré gauge theory of gravity: Friedman cosmology with even and odd parity modes: Analytic part

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 83, Issue 2, 2011, Pages

  Baekler, Peter ^a   Hehl, Friedrich W ^b,d   Nester, James M ^c  

^a UNIVERSITY OF APPLIED SCIENCES   (Germany)

^b UNIVERSITY OF COLOGNE   (Germany)

^c NATIONAL CENTRAL UNIVERSITY   (Taiwan)

^d UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551511465     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.83.024001     Document Type: Article

References (114)

1. D.W. Sciama, in Festschrift for Infeld (Pergamon Press, Oxford; PWN, Warsaw, 1962), p.c 415.
2. T.W.B. Kibble, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 2, 212 (1961). 10.1063/1.1703702
3. F.W. Hehl, in Proc. of the 6th Course of the School of Cosmology and Gravitation on Spin, Torsion, Rotation, and Supergravity, held at Erice, Italy, 1979 edited by, P.G. Bergmann, and, V. de Sabbata, (Plenum, New York, 1980), p. 5, http://www.thp.uni-koeln.de/gravitation/mitarbeiter/Erice1979.pdf.
4. K. Hayashi and T. Shirafuji, Prog. Theor. Phys. 64, 866 (1980); PTPKAV 0033-068X
5. K. Hayashi T. Shirafuji Prog. Theor. Phys. 65, 2079E (1981); PTPKAV 0033-068X 10.1143/PTP.65.2079a
6. K. Hayashi T. Shirafuji Prog. Theor. Phys. 64, 883 (1980); PTPKAV 0033-068X
7. K. Hayashi T. Shirafuji Prog. Theor. Phys. 65, 2079E (1981); PTPKAV 0033-068X 10.1143/PTP.65.2079b
8. K. Hayashi T. Shirafuji Prog. Theor. Phys. 64, 1435 (1980); PTPKAV 0033-068X 10.1143/PTP.64.1435
9. K. Hayashi T. Shirafuji Prog. Theor. Phys. 66, 741(E) (1981); PTPKAV 0033-068X 10.1143/PTP.66.741
10. K. Hayashi T. Shirafuji Prog. Theor. Phys. 64, 2222 (1980); PTPKAV 0033-068X 10.1143/PTP.64.2222
11. K. Hayashi T. Shirafuji Prog. Theor. Phys. 65, 525 (1981). PTPKAV 0033-068X 10.1143/PTP.65.525
12. J.M. Nester, in Proceedings of Workshop on Kaluza-Klein theories, Chalk River/Deep River, Ontario, 1983, edited by, H.C. Lee, (World Scientific, Singapore, 1984), p. 83.
13. E.W. Mielke, Geometrodynamics of Gauge Fields (Akademie-Verlag, Berlin, 1987).
14. F. Gronwald and F.W. Hehl, in Proc. Int. School of Cosm. & Gravit. 14th Course: Quantum Gravity. Held in Erice, Italy. Proceedings, edited by, P.G. Bergmann, (World Scientific, Singapore, 1996), p. 148;
15. F. Gronwald F.W. Hehl http://arxiv.org/abs/gr-qc/9602013.
16. M. Blagojević, Gravitation and Gauge Symmetries (IoP Publishing, Bristol, 2002).
17. T. Ortín, Gravity and Strings (Cambridge University Press, Cambridge, UK, 2004).
18. L. Ryder, Introduction to General Relativity (Cambridge University Press, Cambridge, UK, 2009).
19. K.F. Shie, J.M. Nester, and H.J. Yo, Phys. Rev. D PRVDAQ 1550-7998 78, 023522 (2008). 10.1103/PhysRevD.78.023522
20. H. Chen, F.H. Ho, J.M. Nester, C.H. Wang, and H.J. Yo, J. Cosmol. Astropart. Phys. JCAPBP 1475-7516 10 (2009) 027. 10.1088/1475-7516/2009/10/027
21. Yu. N. Obukhov, V.N. Ponomarev, and V.V. Zhytnikov, Gen. Relativ. Gravit. GRGVA8 0001-7701 21, 1107 (1989). 10.1007/BF00763457
22. F.W. Hehl, J.D. McCrea, E.W. Mielke, and Y. Ne'eman, Phys. Rep. PRPLCM 0370-1573 258, 1 (1995). 10.1016/0370-1573(94)00111-F
23. F.W. Hehl and Yu. N. Obukhov, Foundations of Classical Electrodynamics-Charge, flux, and metric (Birkhäuser, Boston, MA, 2003).
24. P. Baekler, N. Boulanger, and F.W. Hehl, Phys. Rev. D PRVDAQ 1550-7998 74, 125009 (2006). 10.1103/PhysRevD.74.125009 (Pubitemid 44932089)
25. R.P. Wallner, Gen. Relativ. Gravit. GRGVA8 0001-7701 17, 1081 (1985). 10.1007/BF00774210
26. J.D. McCrea, Classical Quantum Gravity CQGRDG 0264-9381 9, 553 (1992). 10.1088/0264-9381/9/2/018
27. Y.N. Obukhov, Int. J. Geom. Methods Mod. Phys. 0219-8878 3, 95 (2006). 10.1142/S021988780600103X (Pubitemid 44120893)
28. D. Vassiliev, Ann. Phys. (Berlin) ANPYA2 0003-3804 14, 231 (2005). 10.1002/andp.200410118 (Pubitemid 41359372)
29. V. Pasic and D. Vassiliev, Classical Quantum Gravity CQGRDG 0264-9381 22, 3961 (2005). 10.1088/0264-9381/22/19/010 (Pubitemid 41367770)
30. F. Halbwachs, Théorie relativiste des fluides à spin (Gauthier Villars, Paris, 1960).
31. Y.N. Obukhov and R. Tresguerres, Phys. Lett. A 184, 17 (1993). PYLAAG 0375-9601 10.1016/0375-9601(93)90339-2
32. Y.N. Obukhov, Phys. Lett. A 210, 163 (1996). PYLAAG 0375-9601 10.1016/S0375-9601(96)80004-1 (Pubitemid 126405428)
33. A. Trautman, in: Encyclopedia of Math. Physics, edited by, J.-P. Francoise, (Elsevier, Oxford, 2006), p. 189.
34. M.O. Ribas and G.M. Kremer, Gravitation Cosmol. GRCOF6 0202-2893 16, 173 (2010). 10.1134/S020228931002012X
35. B.P. Dolan, Classical Quantum Gravity CQGRDG 0264-9381 27, 095010 (2010). 10.1088/0264-9381/27/9/095010
36. I.L. Shapiro, Phys. Rep. PRPLCM 0370-1573 357, 113 (2002). 10.1016/S0370-1573(01)00030-8
37. W.-T. Ni, Rep. Prog. Phys. 73, 056901 (2010). RPPHAG 0034-4885 10.1088/0034-4885/73/5/056901
38. W. Esser, Diploma Thesis University of Cologne, 1996.
39. F.W. Hehl and A. Macias, Int. J. Mod. Phys. D 8, 399 (1999). IMPDEO 0218-2718 10.1142/S0218271899000316
40. E. Sezgin and P. van Nieuwenhuizen, Phys. Rev. D PRVDAQ 0556-2821 21, 3269 (1980). 10.1103/PhysRevD.21.3269
41. R. Kuhfuss and J. Nitsch, Gen. Relativ. Gravit. GRGVA8 0001-7701 18, 1207 (1986). 10.1007/BF00763447
42. Y.M. Cho, D.G. Pak, and B.S. Park, Int. J. Mod. Phys. A 25, 2867 (2010). IMPAEF 0217-751X 10.1142/S0217751X10048524
43. M. Blagojevic and I.A. Nikolic, Phys. Rev. D PRVDAQ 0556-2821 28, 2455 (1983). 10.1103/PhysRevD.28.2455
44. I.A. Nikolić, Phys. Rev. D PRVDAQ 0556-2821 30, 2508 (1984). 10.1103/PhysRevD.30.2508
45. R.D. Hecht, J.M. Nester, and V.V. Zhytnikov, Phys. Lett. A 222, 37 (1996). PYLAAG 0375-9601 10.1016/0375-9601(96)00622-6
46. H. Chen, J.M. Nester, and H.J. Yo, Acta Phys. Pol. B APOBBB 0587-4254 29, 961 (1998).
47. H.J. Yo and J.M. Nester, Int. J. Mod. Phys. D 8, 459 (1999). IMPDEO 0218-2718 10.1142/S021827189900033X
48. H.J. Yo and J.M. Nester, Int. J. Mod. Phys. D 11, 747 (2002). IMPDEO 0218-2718 10.1142/S0218271802001998
49. T. Frankel, The Geometry of Physics-An Introduction (Cambridge University Press, Cambridge, 2004) 2nd ed.
50. M.S. Sozzi, Discrete Symmetries and C P Violation (Oxford University Press, Oxford, UK, 2008);
51. We quote: "11.3 The cosmic connection. The issue of C P violation, the smallest symmetry violation detected so far, is not only relevant for the understanding of a small set of relatively rare weak processes; on the contrary it actually bears on one of the most intriguing mysteries of cosmology, namely the fact that the universe is almost empty but not exactly so, allowing our own existence. 11.3.1 The matter-antimatter asymmetry. The fundamental and deep connection between particles and antiparticles which is expressed by C P T symmetry, the only symmetry which (so far) appears to be exactly valid in Nature, and also by the C or C P symmetries valid for the dominant interactions of Nature, could lead to the expectation that matter and antimatter, being on equal footing, are equally abundant in the universe. In his 1933 Nobel lecture, P.A.M. Dirac said that 'we must regard it rather as an accident that the Earth (and presumably the whole solar system), contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars it is the other way about[...] In fact, there may be half the stars of each kind.' This appears, however, not to be the case and only one of the two, which we call matter, is present around us (Steigman, 1976). Antiparticles are found in Nature in tiny amounts, created together with particles in (natural or artificial) high energy processes, but they do not appear to be present in significant amounts in the form of stable macroscopic lumps of antimatter*..." *)While antimatter is very scarce in the universe, antiparticles are present even in the human body: out of about 100 g of potassium, 0.02% is in the form of the radioactive isotope K 40, which has a β ⊃+ decay with a half-life of 1.3 billion years.
52. J. Leitner and S. Okubo, Phys. Rev. 136, B1542 (1964). PHRVAO 0031-899X 10.1103/PhysRev.136.B1542
53. K. Hayashi, Phys. Lett. B 43, 497 (1973). PYLBAJ 0370-2693 10.1016/0370-2693(73)90355-9
54. N.D. Hari Dass, Ann. Phys. (N.Y.) APNYA6 0003-4916 107, 337 (1977). 10.1016/0003-4916(77)90215-9
55. R. Hojman, C. Mukku, and W.A. Sayed, Phys. Rev. D PRVDAQ 0556-2821 22, 1915 (1980). 10.1103/PhysRevD.22.1915
56. C. Mukku, Special issue on Torsion, edited by, V. Dvoeglazov, [Annales de la Fondation Louis de Broglie 32, 311 (2007)]. AFLBDU 0182-4295
57. P.C. Nelson, Phys. Lett. A 79, 285 (1980). PYLAAG 0375-9601 10.1016/0375-9601(80)90348-5
58. H.T. Nieh and M.L. Yan, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 23, 373 (1982). 10.1063/1.525379
59. H.T. Nieh, Int. J. Mod. Phys. A 22, 5237 (2007). IMPAEF 0217-751X 10.1142/S0217751X07038414
60. F.W. Hehl and J.D. McCrea, Found. Phys. 16, 267 (1986). FNDPA4 0015-9018 10.1007/BF01889477
61. J.D. McCrea, F.W. Hehl, and E.W. Mielke, Int. J. Theor. Phys. 29, 1185 (1990). IJTPBM 0020-7748 10.1007/BF00672931
62. P. Baekler, E.W. Mielke, and F.W. Hehl, Nuovo Cimento 107B, 91 (1992). NUCIAD 0029-6341 10.1007/BF02726888
63. Y.N. Obukhov and F.W. Hehl, Acta Phys. Pol. B APOBBB 0587-4254 27, 2685 (1996).
64. C. Kiefer, Quantum Gravity (Oxford University Press, Oxford, UK, 2007), 2nd ed..
65. C. Rovelli, Quantum Gravity (Cambridge University press, Cambridge, UK, 2004).
66. S. Holst, Phys. Rev. D PRVDAQ 0556-2821 53, 5966 (1996). 10.1103/PhysRevD.53.5966
67. L. Freidel, D. Minic, and T. Takeuchi, Phys. Rev. D PRVDAQ 1550-7998 72, 104002 (2005). 10.1103/PhysRevD.72.104002
68. L. Freidel, J. Kowalski-Glikman, and A. Starodubtsev, Phys. Rev. D PRVDAQ 1550-7998 74, 084002 (2006). 10.1103/PhysRevD.74.084002 (Pubitemid 44498347)
69. I.B. Khriplovich and A.A. Pomeransky, Phys. Rev. D PRVDAQ 1550-7998 73, 107502 (2006). 10.1103/PhysRevD.73.107502
70. M. Bojowald and R. Das, Phys. Rev. D PRVDAQ 1550-7998 78, 064009 (2008). 10.1103/PhysRevD.78.064009
71. B. Mukhopadhyaya and S. Sengupta, Phys. Lett. B 458, 8 (1999). PYLBAJ 0370-2693 10.1016/S0370-2693(99)00605-X
72. B. Mukhopadhyaya, S. Sen, S. SenGupta, and S. Sur, Eur. Phys. J. C 35, 129 (2004). EPCFFB 1434-6044 10.1140/epjc/s2004-01759-7 (Pubitemid 38830187)
73. E.W. Mielke, Gen. Relativ. Gravit. GRGVA8 0001-7701 40, 1311 (2008). 10.1007/s10714-007-0603-3
74. E.W. Mielke, Phys. Rev. D PRVDAQ 1550-7998 80, 067502 (2009). 10.1103/PhysRevD.80.067502
75. N.J. Poplawski, arXiv:1005.0893.
76. A. Randono, Classical Quantum Gravity CQGRDG 0264-9381 27, 215019 (2010). 10.1088/0264-9381/27/21/215019
77. J.D. Bjorken, arXiv:1008.0033.
78. R. Jackiw and S.-Y. Pi, Phys. Rev. D PRVDAQ 0556-2821 68, 104012 (2003). 10.1103/PhysRevD.68.104012 (Pubitemid 44628627)
79. M.B. Cantcheff, Phys. Rev. D PRVDAQ 1550-7998 78, 025002 (2008). 10.1103/PhysRevD.78.025002
80. U. Ertem, arXiv:0912.1433.
81. H.J. Yo and J.M. Nester, Mod. Phys. Lett. A 22, 2057 (2007). MPLAEQ 0217-7323 10.1142/S0217732307025303
82. X.-z. Li, C.-b. Sun, and P. Xi, Phys. Rev. D PRVDAQ 1550-7998 79, 027301 (2009). 10.1103/PhysRevD.79.027301
83. X.-z. Li, C.-b. Sun, and P. Xi, J. Cosmol. Astropart. Phys. JCAPBP 1475-7516 04 (2009) 015. 10.1088/1475-7516/2009/04/015
84. G. Steigman, Annu. Rev. Astron. Astrophys. ARAAAJ 0066-4146 14, 339 (1976). 10.1146/annurev.aa.14.090176.002011
85. A.C. Hearn REDUCE User's Manual, Version 3.5 RAND Publication CP78 (Rev. 10/93) (The RAND Corporation, Santa Monica, CA, USA, 1993). Nowadays, Reduce is freely available for download; for details, see http://reduce-algebra.com/.
86. E. Schrüfer, EXCALC: A System for Doing Calculations in the Calculus of Modern Differential Geometry (GMD-SCAI, D-53757 St. Augustin, Germany, 1994).
87. E. Schrüfer, F.W. Hehl, and J.D. McCrea, Gen. Relativ. Gravit. GRGVA8 0001-7701 19, 197 (1987). 10.1007/BF00770331
88. J. Socorro, A. Macias, and F.W. Hehl, Comput. Phys. Commun. 115, 264 (1998). CPHCBZ 0010-4655 10.1016/S0010-4655(98)00133-7
89. F. Müller-Hoissen and J. Nitsch, Phys. Rev. D PRVDAQ 0556-2821 28, 718 (1983). 10.1103/PhysRevD.28.718
90. P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, UK, 1930).
91. J.A. Schouten, Tensor Analysis for Physicists (Dover, New York, 1989), 2nd ed..
92. W. Kopczyński, Phys. Lett. A 43, 63 (1973). PYLAAG 0375-9601 10.1016/0375-9601(73)90546-X
93. A. Trautman, Nature (London), Phys. Sci. NPSCA6 0300-8746 242, 7 (1973). 10.1038/242007b0
94. J. Tafel, Phys. Lett. A 45, 341 (1973). PYLAAG 0375-9601 10.1016/0375-9601(73)90108-4
95. B. Kuchowicz, Acta Cosmologica Z 3, 109 (1975);
96. B. Kuchowicz Acta Cosmologica Z 4, 67 (1976).
97. B. Kuchowicz, Astrophys. Space Sci. 39, 157 (1976); APSSBE 0004-640X 10.1007/BF00640517
98. B. Kuchowicz Astrophys. Space Sci. 40, 167 (1976). APSSBE 0004-640X 10.1007/BF00651197
99. G.D. Kerlick, Ann. Phys. (N.Y.) APNYA6 0003-4916 99, 127 (1976). 10.1016/0003-4916(76)90086-5
100. P. Baekler and F.W. Hehl, Lect. Notes Phys. LNPHA4 0075-8450 176, 1 (1983); 10.1007/3-540-11994-9-1
101. P. Baekler F.W. Hehl in Proceedings of the International Symposium on Gauge Theory and Gravitation (g & G) held at Tezukayama University Nara, Japan (Springer, Berlin, 1983).
102. A. Canale, R. de Ritis, and C. Tarantino, Phys. Lett. A 100, 178 (1984). PYLAAG 0375-9601 10.1016/0375-9601(84)90754-0
103. A.V. Minkevich, Phys. Lett. A 80, 232 (1980); PYLAAG 0375-9601 10.1016/0375-9601(80)90008-0
104. A.V. Minkevich Phys. Lett. A 95, 422 (1983); PYLAAG 0375-9601 10.1016/0375-9601(83)90309-2
105. A.V. Minkevich and I.M. Nemenman, Classical Quantum Gravity CQGRDG 0264-9381 12, 1259 (1995); 10.1088/0264-9381/12/5/015
106. A.V. Minkevich, A.S. Garkun, and V.I. Kudin, Classical Quantum Gravity CQGRDG 0264-9381 24, 5835 (2007). 10.1088/0264-9381/24/23/007
107. D. Puetzfeld, New Astron. Rev. 49, 59 (2005). NAREF9 1387-6473 10.1016/j.newar.2005.01.022 (Pubitemid 40621150)
108. H. Goenner and F. Müller-Hoissen, Classical Quantum Gravity CQGRDG 0264-9381 1, 651 (1984). 10.1088/0264-9381/1/6/010
109. P. Baekler, Ph.D. thesis, University of Cologne, Germany, 1986.
110. I. Cartan, C.R. Hebd. Seances Acad. Sci. COREAF 0001-4036 174, 593 (1922).
111. M. Lazar and F.W. Hehl, Found. Phys. 40, 1298 (2010). FNDPA4 0015-9018 10.1007/s10701-010-9440-4
112. X.-c. Ao, X.-z. Li, and P. Xi, Phys. Lett. B 694, 186 (2010). PYLBAJ 0370-2693 10.1016/j.physletb.2010.09.060
113. J.D. Bekenstein, Phys. Rev. D PRVDAQ 1550-7998 70, 083509 (2004); 10.1103/PhysRevD.70.083509 (Pubitemid 44947542)
114. J.D. Bekenstein Phys. Rev. D PRVDAQ 1550-7998 71, 069901(E) (2005). 10.1103/PhysRevD.71.069901