Chern-Simons modified general relativity

Physics Reports

Volumn 480, Issue 1-2, 2009, Pages 1-55

  Alexander, Stephon ^a,c   Yunes, Nicolás ^b,c  

^a HAVERFORD COLLEGE   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Chern; Loop Quantum Gravity; Parity violation; Simons; String theory

Indexed keywords

EID: 68349120396     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2009.07.002     Document Type: Review

References (191)

1. J. Dunkley, et al., Five-year Wilkinson microwave anisotropy probe (WMAP) observations: Likelihoods and parameters from the WMAP data. arXiv:0803.0586
2. Wittman D.M., Tyson J.A., Kirkman D., Dell'antonio I., and Bernstein G. Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales. Nature 405 (2000) 143-149 10.1038/35012001 arXiv:astro-ph/0003014
3. Markevitch M., Forman W.R., Sarazin C.L., and Vikhlinin A. The temperature structure of 30 nearby clusters observed with ASCA. Similarity of temperature profiles. Astrophys. J. 503 (1998) 77 10.1086/305976 arXiv:astro-ph/9711289
4. Riess A.G. Type Ia supernova discoveries at z > 1 From the Hubble space telescope: Evidence for past deceleration and constraints on dark energy evolution. Astrophys. J. 607 (2004) 665-687 10.1086/383612 arXiv:astro-ph/0402512
5. Svrcek P., and Witten E. Axions in string theory. Journal of High Energy Physics 06 (2006) 051 arXiv:hep-th/0605206
6. S. Alexander, N. Yunes, Chern-Simons modified gravity as a torsion theory and its interaction with Fermions. arXiv:0804.1797
7. Alexander S., and Yunes N. Parametrized post-Newtonian expansion of Chern-Simons gravity. Phys. Rev. D 75 (2007) 124022 arXiv:arXiv:0704.0299[hep-th]
8. C.-Y. Sun, D.-H. Zhang, A cyclic cosmological model in the landscape scenario. arXiv:hep-th/0611101
9. Wesley D.H., Steinhardt P.J., and Turok N. Controlling chaos through compactification in cosmological models with a collapsing phase. Phys. Rev. D 72 (2005) 063513 10.1103/PhysRevD.72.063513 arXiv:hep-th/0502108
10. Brandenberger R., Easson D.A., and Kimberly D. Loitering phase in brane gas cosmology. Nucl. Phys. B 623 (2002) 421-436 arXiv:hep-th/0109165
11. Battefeld T., and Watson S. String gas cosmology. Rev. Modern Phys. 78 (2006) 435-454 10.1103/RevModPhys.78.435 arXiv:hep-th/0510022
12. Brandenberger R.H., Nayeri A., Patil S.P., and Vafa C. String gas cosmology and structure formation. Internat. J. Modern Phys. A 22 (2007) 3621-3642 10.1142/S0217751X07037159 arXiv:hep-th/0608121
13. Brandenberger R.H. String gas cosmology and structure formation: A brief review. Modern Phys. Lett. A 22 (2007) 1875-1885 10.1142/S0217732307025091 arXiv:hep-th/0702001
14. Brax P., Van bruck C.de., and Davis A.-C. Brane world cosmology. Rep. Progr. Phys. 67 (2004) 2183-2232 10.1088/0034-4885/67/12/R02 arXiv:hep-th/0404011
15. Alexander S., Brandenberger R.H., and Easson D. Brane gases in the early universe. Phys. Rev. D 62 (2000) 103509 arXiv:hep-th/0005212
16. Tseytlin A.A., and Vafa C. Elements of string cosmology. Nucl. Phys. B 372 (1992) 443-466 10.1016/0550-3213(92)90327-8 arXiv:hep-th/9109048
17. Nayeri A., Brandenberger R.H., and Vafa C. Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology. Phys. Rev. Lett. 97 (2006) 021302 10.1103/PhysRevLett.97.021302 arXiv:hep-th/0511140
18. Carroll S.M. Lecture notes on general relativity. arXiv:gr-qc/9712019
19. Carroll S.M. Spacetime and Geometry: An Introduction to General Relativity (2004), Addison-Wesley, San Francisco, USA p. 513
20. Wald R.M. General Relativity (1984), The University of Chicago Press
21. Misner C.W., Thorne K., and Wheeler J.A. Gravitation (1973), W.H. Freeman Co., San Francisco
22. Jackiw R., and Pi S.Y. Chern-simons modification of general relativity. Phys. Rev. D 68 (2003) 104012 arXiv/gr-qc/0308071
23. Campbell B.A., Duncan M.J., Kaloper N., and Olive K.A. Gravitational dynamics with Lorentz Chern-Simons terms. Nucl. Phys. B 351 (1991) 778-792 10.1016/S0550-3213(05)80045-8
24. Campbell B.A., Kaloper N., Madden R., and Olive K.A. Physical properties of four-dimensional superstring gravity black hole solutions. Nucl. Phys. B 399 (1993) 137-168 10.1016/0550-3213(93)90620-5 arXiv:hep-th/9301129
25. Deser S., Jackiw R., and Templeton S. Topologically massive gauge theories. Ann. Phys. 140 (1982) 372-411 10.1016/0003-4916(82)90164-6
26. Deser S., Jackiw R., and Templeton S. Three-dimensional massive gauge theories. Phys. Rev. Lett. 48 (1982) 975-978 10.1103/PhysRevLett.48.975
27. Alexander S.H.S., Gates J., and James S. Can the string scale be related to the cosmic baryon asymmetry?. Journal of Cosmology and Astroparticle Physics 0606 (2006) 018 arXiv:hep-th/0409014
28. Alexander S.H.-S., Peskin M.E., and Sheikh-Jabbari M.M. Leptogenesis from gravity waves in models of inflation. Phys. Rev. Lett. 96 (2006) 081301 10.1103/PhysRevLett.96.081301 arXiv:hep-th/0403069
29. Alexander S., and Martin J. Birefringent gravitational waves and the consistency check of inflation. Phys. Rev. D 71 (2005) 063526 arXiv:hep-th/0410230
30. Alexander S.H.S. Is cosmic parity violation responsible for the anomalies in the WMAP data?. arXiv:hep-th/0601034
31. Alexander S.H.-S., Peskin M.E., and Sheikh-Jabbari M.M. Gravi-leptogenesis: Leptogenesis from gravity waves in pseudo-scalar driven inflation models. arXiv:hep-ph/0701139
32. Alexander S., and Yunes N. A new PPN parameter to test Chern-Simons gravity. Phys. Rev. Lett. 99 (2007) 241101 10.1103/PhysRevLett.99.241101 arXiv:hep-th/0703265
33. S. Alexander, L.S. Finn, N. Yunes, A gravitational-wave probe of effective quantum gravity. arXiv:arXiv:0712.2542[gr-qc]
34. Yunes N., and Sopuerta C.F. Perturbations of Schwarzschild black holes in Chern-Simons modified gravity. Phys. Rev. D 77 (2008) 064007 10.1103/PhysRevD.77.064007 arXiv:0712.1028
35. Grumiller D., and Yunes N. How do black holes spin in Chern-Simons modified gravity?. Phys. Rev. D 77 (2008) 044015 10.1103/PhysRevD.77.044015 arXiv:0711.1868
36. S. Alexander, R. O'shaughnessy, B.J. Owen, N. Yunes, in progress
37. Smith T.L., Erickcek A.L., Caldwell R.R., and Kamionkowski M. The effects of Chern-Simons gravity on bodies orbiting the earth. Phys. Rev. D 77 (2008) 024015 10.1103/PhysRevD.77.024015 arXiv:0708.0001
38. Garcia A., Hehl F.W., Heinicke C., and Macias A. The Cotton tensor in Riemannian spacetimes. Classical Quantum Gravity 21 (2004) 1099-1118 arXiv:gr-qc/0309008
39. Grumiller D., Mann R., and Mcnees R. Dirichlet boundary value problem for Chern-Simons modified gravity. arXiv:0803.1485
40. D. Grumiller, Private communication
41. Penrose R., and Rindler W. Spinors and Space-Time II (1986), Cambridge University Press
42. Stephani H., Kramer D., Maccallum M., Hoenselaers C., and Herlt E. Exact Solutions of Einstein's field Equations (2003), Cambridge University Press
43. Yunes N., and Gonzalez J.A. Metric of a tidally perturbed spinning black hole. Phys. Rev. D 73 (2006) 024010 arXiv:gr-qc/0510076
44. Cherubini C., Bini D., Capozziello S., and Ruffini R. Second order scalar invariants of the Riemann tensor: Applications to black hole spacetimes. Internat. J. Modern Phys. D 11 (2002) 827-841 arXiv:gr-qc/0302095
45. Matte A. Sur de nouvelles solutions oscillatoires des équations de la gravitation. Canad. J. Math. 5 (1953) 1
46. Regge T., and Wheeler J.A. Stability of a schwarzschild singularity. Phys. Rev. 108 (1957) 1063-1069 10.1103/PhysRev.108.1063
47. Mann R.B., and Marolf D. Holographic renormalization of asymptotically flat spacetimes. Classical Quantum Gravity 23 (2006) 2927-2950 arXiv:hep-th/0511096
48. Mann R.B., Marolf D., and Virmani A. Covariant counterterms and conserved charges in asymptotically flat spacetimes. Classica Quantum Gravity 23 (2006) 6357-6378 arXiv:gr-qc/0607041
49. Fujikawa K. Path integral measure for Gauge invariant Fermion theories. Phys. Rev. Lett. 42 (1979) 1195 10.1103/PhysRevLett.42.1195
50. Fujikawa K. Path integral for Gauge theories with Fermions. Phys. Rev. D 21 (1980) 2848 10.1103/PhysRevD.21.2848
51. Adler S.L. Axial-vector vertex in Spinor electrodynamics. Phys. Rev. 177 (1969) 2426-2438 10.1103/PhysRev.177.2426
52. Bell J.S., and Jackiw R. A PCAC puzzle: pi0 → gamma gamma in the sigma model. Nuovo Cimento A 60 (1969) 47-61
53. Mariz T., Nascimento J.R., Passos E., and Ribeiro R.F. Chern-Simons-like action induced radiatively in general relativity. Phys. Rev. D 70 (2004) 024014 10.1103/PhysRevD.70.024014 arXiv:hep-th/0403205
54. Mariz T., Nascimento J.R., Petrov A.Y., Santos L.Y., and Silva A.J.da. Lorentz violation and the proper-time method. Phys. Lett. B 661 (2008) 312-318 10.1016/j.physletb.2007.10.089 arXiv:0708.3348
55. Gomes M. On the ambiguities in the effective action in Lorentz- violating gravity. Phys. Rev. D 78 (2008) 025029 10.1103/PhysRevD.78.025029 arXiv:0805.4409
56. Alvarez-Gaume L., and Witten E. Gravitational anomalies. Nuclear Phys. B 234 (1984) 269
57. Green M.B., Schwarz J.H., and Witten E. Superstring Theory, Vol. 1: Introduction (1987), Cambridge University Press
58. Green M.B., Schwarz J.H., and Witten E. Superstring Theory. Vol. 2: Loop Amplitides Anomalies Phenomenology. Cambridge Monographs On Mathematical Physics (1987), Cambridge University Press, Cambridge, UK
59. Polchinski J. String Theory. Vol. 2: Superstring Theory and Beyond (1998), Univ. Pr., Cambridge, UK p. 531
60. Gukov S., Kachru S., Liu X., and Mcallister L. Heterotic moduli stabilization with fractional Chern-Simons invariants. Phys. Rev. D 69 (2004) 086008 10.1103/PhysRevD.69.086008 arXiv:hep-th/0310159
61. Bergshoeff E., Roo M.de., Wit B.de., and Van nieuwenhuizen P. Ten-dimensional Maxwell-Einstein supergravity, its currents, and the issue of its auxiliary fields. Nuclear Phys. B 195 (1982) 97-136 10.1016/0550-3213(82)90050-5
62. Green M.B., and Schwarz J.H. Anomaly cancellation in supersymmetric D = 10 Gauge theory and superstring theory. Phys. Lett. B 149 (1984) 117-122 10.1016/0370-2693(84)91565-X
63. Ashtekar A., and Lewandowski J. Background independent quantum gravity: A status report. Classica Quantum Gravity 21 (2004) R53 10.1088/0264-9381/21/15/R01 arXiv:gr-qc/0404018
64. Thiemann T. Introduction to modern canonical quantum general relativity. arXiv:gr-qc/0110034
65. C. Rovelli, Quantum Gravity, Univ. Pr, Cambridge, UK, p. 455
66. Yang C.-N., and Mills R.L. Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96 (1954) 191-195 10.1103/PhysRev.96.191
67. A. Ashtekar, Lectures on Nonperturbative Canonical Gravity, in: Advanced Series in Astrophysics and Cosmology, vol. 6, World Scientific, Singapore, Singapore, p. 334
68. Barbero J.F. Real Ashtekar variables for Lorentzian signature space times. Phys. Rev. D 51 (1995) 5507-5510 10.1103/PhysRevD.51.5507 arXiv:gr-qc/9410014
69. Holst S. Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action. Phys. Rev. D 53 (1996) 5966-5969 10.1103/PhysRevD.53.5966 arXiv:gr-qc/9511026
70. Ashtekar A., and Balachandran A.P. S.Jo. The CP problem in quantum gravity. Internat. J. Modern Phys. A 4 (1989) 1493 10.1142/S0217751X89000649
71. Taveras V., and Yunes N. The Barbero-Immirzi parameter as a scalar field: K-Inflation from loop quantum gravity?. Phys. Rev. D 78 (2008) 064070 10.1103/PhysRevD.78.064070 arXiv:0807.2652
72. Immirzi G. Real and complex connections for canonical gravity. Classica Quantum Gravity 14 (1997) L177-L181 arXiv:gr-qc/9612030
73. Perez A., and Rovelli C. Physical effects of the Immirzi parameter. Phys. Rev. D 73 (2006) 044013 arXiv:gr-qc/0505081
74. Freidel L., Minic D., and Takeuchi T. Quantum gravity torsion parity violation and all that. Phys. Rev. D 72 (2005) 104002 10.1103/PhysRevD.72.104002 arXiv:hep-th/0507253
75. Randono A. A note on parity violation and the Immirzi parameter. arXiv:hep-th/0510001
76. Mercuri S. From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional. Phys. Rev. D 77 (2008) 024036 arXiv:0708.0037
77. Mercuri S. Nieh-Yan invariant and fermions in Ashtekar-Barbero- Immirzi formalism. arXiv:gr-qc/0610026
78. Mercuri S. Peccei-Quinn mechanism in gravity and the nature of the Barbero-Immirzi parameter. arXiv:0902.2764
79. Mercuri S. A possible topological interpretation of the Barbero-Immirzi parameter. arXiv:0903.2270
80. Mercuri S., and Taveras V. Interaction of the Barbero-Immirzi field with matter and pseudo-scalar perturbations. arXiv:0903.4407
81. Guarrera D., and Hariton A.J. Papapetrou energy-momentum tensor for Chern-Simons modified gravity. Phys. Rev. D 76 (2007) 044011 arXiv:gr-qc/0702029
82. Gerlach U.H., and Sengupta U.K. Gauge invariant perturbations on most general spherically symmetric space-times. Phys. Rev. D 19 (1979) 2268-2272
83. Gerlach U.H., and Sengupta U.K. Gauge invariant coupled gravitational, acoustical, and electromagnetic modes on most general spherical space-times. Phys. Rev. D 22 (1980) 1300-1312
84. Yunes N., and Pretorius F. Dynamical Chern-Simons modified gravity I: Spinning black holes in the slow-rotation approximation. Phys. Rev. D 79 (2008) 084043 10.1103/PhysRevD.79.084043 arXiv:0902.4669
85. Campbell B.A., Duncan M.J., Kaloper N., and Olive K.A. Axion hair for Kerr black holes. Phys. Lett. B 251 (1990) 34-38 10.1016/0370-2693(90)90227-W
86. Campbell B.A., Kaloper N., and Olive K.A. Axion hair for dyon black holes. Phys. Lett. B 263 (1991) 364-370 10.1016/0370-2693(91)90474-5
87. Reuter M. A Mechanism generating axion hair for Kerr black holes. Classica Quantum Gravity 9 (1992) 751-756
88. Kaloper N. Lorentz Chern-Simons terms in Bianchi cosmologies and the cosmic no hair conjecture. Phys. Rev. D 44 (1991) 2380-2387 10.1103/PhysRevD.44.2380
89. Dolgov A.D., Khriplovich I.B., and Zakharov V.I. Chiral Boson anomaly in a gravitational field. JETP Lett. 45 (1987) 651-653
90. Dolgov A.D., Khriplovich I.B., Vainshtein A.I., and Zakharov V.I. Photonic chiral current and its anomaly in a gravitational field. Nuclear Phys. B 315 (1989) 138 10.1016/0550-3213(89)90451-3
91. Lukács B., and Perjés Z. Note on conformastat vacuum space-times. Phys. Lett. A 88 (1982) 267-268
92. Furtado C., Mariz T., Nascimento J.R., Petrov A.Y., and Santos A.F. The Gódel solution in the modified gravity. Phys. Rev. D 79 (2009) 124039 10.1103/PhysRevD.79.124039 arXiv:0906.0554
93. Jordan P., Ehlers J., and Kundt W. Strenge Lösungen der Feldgleichungen der Allgemeinen Relativitätstheorie. Akad. Wiss. Lit. (Mainz) Abhandl. Math.-Nat. Kl. 2 (1960) 21
94. Aichelburg P.C., and Sexl R.U. On the gravitational field of a massless particle. Gen. Relativity Gravitation 2 (1971) 303-312
95. Lousto C.O., and Sanchez N.G. The Ultrarelativistic limit of the boosted Kerr-Newman geometry and the scattering of spin 1/2 particles. Nuclear Phys. B 383 (1992) 377-394
96. Balasin H., and Nachbagauer H. The Ultrarelativistic Kerr geometry and its energy momentum tensor. Classica Quantum Gravity 12 (1995) 707-714 arXiv:gr-qc/9405053
97. Balasin H., and Nachbagauer H. Distributional energy momentum tensor of the Kerr-Newman space-time family. Classica Quantum Gravity 11 (1994) 1453-1462 arXiv:gr-qc/9312028
98. Konno K., Matsuyama T., and Tanda S. Does a black hole rotate in Chern-Simons modified gravity?. Phys. Rev. D 76 (2007) 024009 arXiv:arXiv:0706.3080[gr-qc]
99. Sopuerta C.F., and Yunes N. Extreme- and intermediate-mass ratio inspirals in dynamical Chern-Simons modified gravity. arXiv:0904.4501
100. Blanchet L. Gravitational radiation from post-newtonian sources and inspiralling compact binaries. Living Rev. Rel. 9 (2006) 4 and references therein. arXiv:gr-qc/0202016
101. Bender C.M., and Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers 1, Asymptotic Methods and Perturbation Theory (1999), Springer, New York
102. Kevorkian J., and Cole J.D. Multiple Scale and Singular Perturbation Methods (1991), Springer, New York and references therein
103. Yunes N., Tichy W., Owen B.J., and Brügmann B. Binary black hole initial data from matched asymptotic expansions. Phys. Rev. D 74 (2006) 104011 arXiv:gr-qc/0503011
104. Yunes N., and Tichy W. Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions. Phys. Rev. D 74 (2006) 064013 arXiv:gr-qc/0601046
105. Will C.M. Generation of post-Newtonian gravitational radiation via direct integration of the relaxed Einstein equations. Progr. Theoret. Phys. Suppl. 136 (1999) 158-167 10.1143/PTPS.136.158 arXiv:gr-qc/9910057
106. Damour T. Gravitational Radiation (1983), North-Holland, Amsterdam pp. 59-144
107. Lanczos C. Bemerkung zur de sitterschen welt. Phys. Zeits. 23 (1922) 539
108. Lanczos C. Fl' ́achenhafte verteilung der materie in der einsteinschen gravitationsheorie. Ann. Phys. 74 (1924) 528
109. G. Darmois, Les éequations de la gravitation einsteinienne, Mémorial des sciences mathématique XXV
110. Lichnerowicz A. Théories Relativistes de la Gravitation et de l'Electromagnétisme (1955), Masson, Paris
111. Misner C.W., and Sharp D.H. Relativistic equations for adiabatic spherically symmetric gravitational collapse. Phys. Rev. B 136 (1964) 571
112. Barrabes C., and Israel W. Thin shells in general relativity and cosmology: The lightlike limit. Phys. Rev. D 43 (1991) 1129-1142
113. Israel W. Singular hypersurfaces and thin shells in gr. Nuovo Cimento B 44 (1966) 1-14
114. Poisson E. A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics (2004), Cambridge, New York, United States and references therein
115. Will C.M. Theory and Experiment in Gravitational Physics (1993), Cambridge University Press, Cambridge, UK
116. Schiff L.I. Motion of a gyroscope according to Einstein's theory of gravitation. Proc. Natl. Acad. Sci. 46 (1960) 871
117. Nordtvedt K. Equivalence principle for massive bodies. 2. theory. Phys. Rev. 169 (1968) 1017-1025
118. Nordtvedt K.J., and Will C.M. Conservation laws and preferred frames in relativistic gravity. II. Experimental evidence to rule out preferred-frame theories of gravity. The Astrophysical Journal 177 (1972) 775
119. Will C.M. Theoretical frameworks for testing relativistic gravity. II. Parametrized post-Newtonian hydrodynamics, and the Nordtvedt effect. The Astrophysical Journal 163 (1971) 611
120. Will C.M. Relativistic gravity tn the solar system. 111. Experimental disproof of a class of linear theories of gravitation. The Astrophysical Journal 185 (1973) 31-42
121. Will C.M. The confrontation between general relativity and experiment. Living Rev. Rel. 9 (2005) 3 arXiv:gr-qc/0510072
122. Thorne K.S., Price R.H., and Macdonald D.A. Black Holes: The Membrane Paradigm, Black Holes: The Membrane Paradigm (1986)
123. Mashhoon B. Gravitoelectromagnetism: A brief review. arXiv:gr-qc/0311030
124. C.M. Will, The confrontation between general relativity and experiment, Living Reviews in Relativity 9 (3). http://www.livingreviews.org/lrr-2006-3
125. Sopuerta C.F., Yunes N., and Laguna P. Gravitational recoil from binary black hole mergers: The close-limit approximation. Phys. Rev. D 74 (2006) 124010 arXiv:astro-ph/0608600
126. Cunningham C.T., Price R.H., and Moncrief V. Radiation from collapsing relativistic stars. I - Linearized odd-parity radiation. The Astrophysical Journal 224 (1978) 643-667
127. Zerilli F.J. Effective potential for even-parity regge-wheeler gravitational perturbation equations. Physical Review Letters 24 (1970) 737-738
128. Moncrief V. Ann. Phys. (N.Y.) 88 (1974) 323
129. Konno K., Matsuyama T., Asano Y., and Tanda S. Flat rotation curves in Chern-Simons modified gravity. arXiv:0807.0679
130. Ciufolini I. Gravitomagnetism, frame-dragging and lunar laser ranging. arXiv:0704.3338
131. Ciufolini I., and Pavlis E.C. A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature 431 (2004) 958-960 10.1038/nature03007
132. I. Ciufolini, A. Paolozzi, D.G. Currie, E.C. Pavlis, Lares/weber-Sat frame-dragging and fundamental physics, in: Prepared for International Workshop on Frontier Science: Physics and Astrophysics in Space, Frascati and Rome, Italy, 14-19 Jun 2004
133. Konno K., Matsuyama T., and Tanda S. Rotating black hole in extended Chern-Simons modified gravity. arXiv:0902.4767
134. Lue A., Wang L.-M., and Kamionkowski M. Cosmological signature of new parity-violating interactions. Phys. Rev. Lett. 83 (1999) 1506-1509 arXiv:astro-ph/9812088
135. Cantcheff M.B. Einstein-Cartan formulation of Chern-Simons Lorentz violating gravity and holographic structure. Phys. Rev. D 78 (2008) 025002 10.1103/PhysRevD.78.025002 arXiv:0801.0067
136. Romano J.D. Geometrodynamics versus connection dynamics (in the context of (2+1) and (3+1) gravity. Gen. Relativity Gravitation 25 (1993) 759-854 arXiv:gr-qc/9303032
137. Randono A.C. In search of quantum de Sitter space: Generalizing the Kodama state. arXiv:0709.2905
138. Kostelecky V.A. Gravity lorentz violation and the standard model. Phys. Rev. D 69 (2004) 105009 arXiv:hep-th/0312310
139. Belyaev A.S., Shapiro I.L., and Vale M.A.B.do. Torsion phenomenology at the LHC. Phys. Rev. D 75 (2007) 034014 10.1103/PhysRevD.75.034014 arXiv:hep-ph/0701002
140. Kostelecky V.A., Russell N., and Tasson J. New constraints on torsion from Lorentz violation. Phys. Rev. Lett. 100 (2008) 111102 arXiv:0712.4393
141. http://einstein.stanford.edu
142. Will C.M. Covariant calculation of general relativistic effects in an orbiting gyroscope experiment. Phys. Rev. D 67 (2003) 062003 10.1103/PhysRevD.67.062003 arXiv:gr-qc/0212069
143. Yunes N., and Spergel D.N. Double binary pulsar test of dynamical Chern-Simons modified gravity. arXiv:0810.5541
144. Jones D.I., and Andersson N. Gravitational waves from freely precessing neutron stars. Mon. Not. Roy. Astron. Soc. 331 (2002) 203 10.1046/j.1365-8711.2002.05180.x arXiv:gr-qc/0106094
145. M. Tegmark, S. Hughes, Private communication
146. Iorio L. An alternative derivation of the periodical and secular Lense-Thirring effect on the orbit of a test body. Nuovo Cimento B 116 (2001) 777-789 arXiv:gr-qc/9908080
147. Murray C.D., and Dermott S.F. Solar System Dynamics (1999), Cambridge University Press, Cambridge
148. R. O'shaughnessy, Private communication
149. Brunfiel G. Nature 444 (2006) 978
150. Burgay M., et al. An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system. Nature 426 (2003) 531-533 10.1038/nature02124 arXiv:astro-ph/0312071
151. Hulse R.A., and Taylor J.H. Discovery of a pulsar in a binary system. Astrophys. J. 195 (1975) L51-L53
152. Montenbruck O., and Gill E. Satellite Orbits. Models Methods Applications (2000), Springer, Germany
153. Kramer M., et al. Tests of general relativity from timing the double pulsar. Science 314 (2006) 97-102 10.1126/science.1132305 arXiv:astro-ph/0609417
154. Rubin V.C., and Ford Jr. W.K.J. Rotation of the Andromeda Nebula from a spectroscopic survey of emission regions. The Astrophysical Journal 159 (1970) 379
155. Rubin V.C., Thonnard N., and Ford Jr. W.K. Rotational properties of 21 SC galaxies with a large range of luminosities and radii, from NGC 4605 /R = 4kpc/ to UGC 2885 /R = 122 kpc/. Astrophys. J. 238 (1980) 471
156. P. Bender, et al., Laser interferometer space antenna for the detection and observation of gravitational waves: An international project in the field of fundamental physics in space, LISA Pre-Phase A Report, Max-Planck-Institut für Quantenoptik, Garching, mPQ 233, July 1998
157. Danzmann K. LISA - an ESA cornerstone mission for a gravitational wave observatory. Classica Quantum Gravity 14 (1997) 1399-1404 10.1088/0264-9381/14/6/002
158. Danzmann K., and Rudiger A. LISA technology - Concept status prospects. Classica Quantum Gravity 20 (2003) S1-S9
159. Sumner T.J., and Shaul D.N.A. The observations of gravitational waves from space using LISA. Modern Physics Letters A 19 11 (2004) 785-800
160. S.M. Merkowitz, J.C. Livas, Laser interferometer space antenna, in: Proceedings, 6th International LISA Symposium, Greenbelt, USA, June 19-23, 2006. Prepared for 6th International LISA Symposium, Greenbelt, Maryland, 19-23 Jun 2006
161. Finn L.S. Detection measurement and gravitational radiation. Phys. Rev. D 46 (1992) 5236-5249 10.1103/PhysRevD.46.5236 arXiv:gr-qc/9209010
162. Finn L.S., and Chernoff D.F. Observing binary inspiral in gravitational radiation: One interferometer. Phys. Rev. D 47 (1993) 2198-2219 10.1103/PhysRevD.47.2198 arXiv:gr-qc/9301003
163. Carroll S.M., Field G.B., and Jackiw R. Limits on a Lorentz and parity violating modification of electrodynamics. Phys. Rev. D 41 (1990) 1231
164. Carroll S.M. Quintessence and the rest of the world. Phys. Rev. Lett. 81 (1998) 3067-3070 arXiv:arXiv:astro-ph/9806099
165. Saito S., Ichiki K., and Taruya A. Probing polarization states of primordial gravitational waves with CMB anisotropies. Journal of Cosmology and Astroparticle Physics 0709 (2007) 002 10.1088/1475-7516/2007/09/002 arXiv:0705.3701
166. Mukhanov V.F., Feldman H.A., and Brandenberger R.H. Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions. Phys. Rept. 215 (1992) 203-333 10.1016/0370-1573(92)90044-Z
167. Martin J., and Schwarz D.J. The precision of slow-roll predictions for the CMBR anisotropies. Phys. Rev. D 62 (2000) 103520 10.1103/PhysRevD.62.103520 arXiv:astro-ph/9911225
168. Gradshteyn I.S., and Ryshik J.M. Table of Integrals Series Products (1980), Academic Press, New York
169. Martin J., and Schwarz D.J. New exact solutions for inflationary cosmological perturbations. Phys. Lett. B 500 (2001) 1-7 10.1016/S0370-2693(01)00071-5 arXiv:astro-ph/0005542
170. Martin J., and Brandenberger R.H. The trans-Planckian problem of inflationary cosmology. Phys. Rev. D 63 (2001) 123501 10.1103/PhysRevD.63.123501 arXiv:hep-th/0005209
171. Lemoine M., Lubo M., Martin J., and Uzan J.-P. The stress-energy tensor for trans-Planckian cosmology. Phys. Rev. D 65 (2002) 023510 10.1103/PhysRevD.65.023510 arXiv:hep-th/0109128
172. Choi K., Hwang J.-C., and Hwang K.W. String theoretic axion coupling and the evolution of cosmic structures. Phys. Rev. D 61 (2000) 084026 10.1103/PhysRevD.61.084026 arXiv:hep-ph/9907244
173. Kamionkowski M., Kosowsky A., and Stebbins A. Statistics of cosmic microwave background polarization. Phys. Rev. D 55 (1997) 7368-7388 10.1103/PhysRevD.55.7368 arXiv:astro-ph/9611125
174. Miller N.J., Shimon M., and Keating B.G. CMB polarization systematics due to beam asymmetry: Impact on cosmological birefringence. arXiv:0903.1116
175. Cabella P., Natoli P., and Silk J. Constraints on CPT violation from WMAP three year polarization data: A wavelet analysis. Phys. Rev. D 76 (2007) 123014 10.1103/PhysRevD.76.123014 arXiv:0705.0810
176. Xia J.-Q., Li H., Wang X.-l., and Zhang X.-M. Testing CPT symmetry with CMB measurements. Astron. Astrophys. 483 (2008) 715-718 10.1051/0004-6361:200809410 arXiv:0710.3325
177. Feng B., Li M., Xia J.-Q., Chen X., and Zhang X. Searching for CPT violation with WMAP and BOOMERANG. Phys. Rev. Lett. 96 (2006) 221302 10.1103/PhysRevLett.96.221302 arXiv:astro-ph/0601095
178. Kamionkowski M. How to de-rotate the cosmic microwave background polarization. Phys. Rev. Lett. 102 (2009) 111302 10.1103/PhysRevLett.102.111302 arXiv:0810.1286
179. Spergel D.N., et al. First year Wilkinson microwave anisotropy probe (WMAP) observations: Determination of cosmological parameters. Astrophys. J. Suppl. 148 (2003) 175 10.1086/377226 arXiv:astro-ph/0302209
180. Huet P., and Sather E. Electroweak baryogenesis and standard model CP violation. Phys. Rev. D 51 (1995) 379-394 10.1103/PhysRevD.51.379 arXiv:hep-ph/9404302
181. Kuzmin V.A., Rubakov V.A., and Shaposhnikov M.E. On the anomalous electroweak Baryon number nonconservation in the early universe. Phys. Lett. B 155 (1985) 36 10.1016/0370-2693(85)91028-7
182. Fukugita M., and Yanagida T. Baryogenesis without grand unification. Phys. Lett. B 174 (1986) 45 10.1016/0370-2693(86)91126-3
183. Sakharov A.D. Violation of CP invariance c asymmetry and Baryon asymmetry of the universe. Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32-35
184. Dimopoulos S., Kachru S., Mcgreevy J., and Wacker J.G. N-flation. Journal of Cosmology and Astroparticle Physics 0808 (2008) 003 10.1088/1475-7516/2008/08/003 arXiv:hep-th/0507205
185. Mcallister L., and Silverstein E. String cosmology: A review. Gen. Relativity Gravitation 40 (2008) 565-605 10.1007/s10714-007-0556-6 arXiv:0710.2951
186. Lyddle R., and Lyth D.H. Cosmological Inflation and Large-Scale Structure (2000), Cambridge University Press, Cambridge
187. Gibbons G.W., and Steif A.R. Anomalous fermion production in gravitational collapse. Phys. Lett. B 314 (1993) 13-20 10.1016/0370-2693(93)91315-E arXiv:gr-qc/9305018
188. A. Linde, Private communication
189. Lyth D.H., Quimbay C., and Rodriguez Y. Leptogenesis and tensor polarisation from a gravitational Chern-Simons term. Journal of High Energy Physics 03 (2005) 016 10.1088/1126-6708/2005/03/016 arXiv:hep-th/0501153
190. Fischler W., and Paban S. Leptogenesis from pseudo-scalar driven inflation. Journal of High Energy Physics 10 (2007) 066 10.1088/1126-6708/2007/10/066 arXiv:0708.3828
191. Richter M.C., Tupper G.B., and Viollier R.D. A symbiotic scenario for the rapid formation of supermassive black holes. Journal of Cosmology and Astroparticle Physics 0612 (2006) 015 arXiv:astro-ph/0611552