Generation of large-scale magnetic fields from inflation in teleparallelism

Journal of Cosmology and Astroparticle Physics

Volumn 2012, Issue 10, 2012, Pages

  Bamba, Kazuharu ^a,c   Geng, Chao Qiang ^b,c,d   Luo, Ling Wei ^b,d  

^a NAGOYA UNIVERSITY   (Japan)

^b NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^c NATIONAL CENTER FOR THEORETICAL SCIENCES   (Taiwan)

^d CHONGQING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

inflation; magnetic fields; modified gravity; primordial magnetic fields

Indexed keywords

EID: 84868235081     PISSN: None     EISSN: 14757516     Source Type: Journal    
DOI: 10.1088/1475-7516/2012/10/058     Document Type: Article

References (144)

1. Supernova Cosmology Project collaboration, S. Perlmutter et al., 1999 Measurements of Ω and Λ from 42 high redshift supernovae, Astrophys. J. 517 565 [astro-ph/9812133]
2. Supernova Search Team collaboration, A.G. Riess et al., 1998 Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 1009 [astro-ph/9805201] (Pubitemid 128138905)
3. SDSS collaboration, M. Tegmark et al., 2004 Cosmological parameters from SDSS and WMAP, Phys. Rev. D 69 103501 [astro-ph/0310723]
4. SDSS collaboration, U. Seljak et al., 2005 Cosmological parameter analysis including SDSS Ly-α forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass and dark energy, Phys. Rev. D 71 103515 [astro-ph/0407372] (Pubitemid 44643242)
5. SDSS collaboration, D.J. Eisenstein et al., 2005 Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies, Astrophys. J. 633 560 [astro-ph/0501171] (Pubitemid 41691965)
6. WMAP collaboration, D. Spergel et al., 2003 First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters, Astrophys. J. Suppl. 148 175 [astro-ph/0302209] (Pubitemid 37395203)
7. WMAP collaboration, D. Spergel et al., 2007 Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology, Astrophys. J. Suppl. 170 377 [astro-ph/0603449]
8. WMAP collaboration, E. Komatsu et al., 2009 Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation, Astrophys. J. Suppl. 180 330 [0803.0547]
9. WMAP collaboration, E. Komatsu et al., 2011 Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation, Astrophys. J. Suppl. 192 18 [1001.4538]
10. B. Jain and A. Taylor, 2003 Cross-correlation tomography: measuring dark energy evolution with weak lensing, Phys. Rev. Lett. 91 141302 [astro-ph/0306046]
11. E.J. Copeland, M. Sami and S. Tsujikawa, 2006 Dynamics of dark energy, Int. J. Mod. Phys. D 15 1753 [hep-th/0603057]
12. R.R. Caldwell and M. Kamionkowski, 2009 The physics of cosmic acceleration, Ann. Rev. Nucl. Part. Sci. 59 397 [0903.0866]
13. L. Amendola and S. Tsujikawa, 2010 Dark energy, Cambridge University Press, Cambridge U.K.
14. S. Tsujikawa, Dark energy: investigation and modeling, [1004.1493]
15. M. Li, X.-D. Li, S. Wang and Y. Wang, 2011 Dark energy, Commun. Theor. Phys. 56 525 [1103.5870]
16. M. Kunz, 2012 The phenomenological approach to modeling the dark energy, Comptes Rendus Physique 13 539 [1204.5482]
17. K. Bamba, S. Capozziello, S. Nojiri and S.D. Odintsov, 2012 Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests, Astrophys. Space Sci. 342 155 [1205.3421]
18. S. Nojiri and S.D. Odintsov, 2011 Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept. 505 59 [1011.0544]
19. S. Nojiri and S.D. Odintsov, 2006 Introduction to modified gravity and gravitational alternative for dark energy eConf C 0602061 06 [hep-th/0601213]
20. S. Nojiri and S.D. Odintsov, 2007 Int. J. Geom. Meth. Mod. Phys. 4 115
21. T.P. Sotiriou and V. Faraoni, 2010 f(R) theories of gravity, Rev. Mod. Phys. 82 451 [0805.1726]
22. A. De Felice and S. Tsujikawa, 2010 f(R) theories Living Rev. Rel. 13 3 [1002.4928]
23. S. Capozziello and V. Faraoni, 2010 Beyond Einstein gravity, Springer, Germany
24. S. Tsujikawa, 2010 Modified gravity models of dark energy, Lect. Notes Phys. 800 99 [1101.0191]
25. T. Clifton, P.G. Ferreira, A. Padilla and C. Skordis, 2012 Modified gravity and cosmology, Phys. Rept. 513 1 [1106.2476]
26. S. Capozziello and M. De Laurentis, 2011 Extended theories of gravity, Phys. Rept. 509 167 [1108.6266]
27. T. Harko and F.S. Lobo, Generalized dark gravity, [1205.3284]
28. S. Capozziello, M. De Laurentis and S.D. Odintsov, 2012 Hamiltonian dynamics and Noether symmetries in extended gravity cosmology, Eur. Phys. J. C 72 2068 [1206.4842]
29. F. Hehl, P. Von Der Heyde, G. Kerlick and J. Nester, 1976 General relativity with spin and torsion: foundations and prospects, Rev. Mod. Phys. 48 393
30. K. Hayashi and T. Shirafuji, 1979 New general relativity, Phys. Rev. D 19 3524 [Addendum ibid D 24 (1982) 3312]
31. E.E. Flanagan and E. Rosenthal, 2007 Can gravity probe B usefully constrain torsion gravity theories?, Phys. Rev. D 75 124016 [0704.1447]
32. J. Garecki, Teleparallel equivalent of general relativity: a critical review, [1010.2654]
33. C.-Q. Geng, C.-C. Lee, E.N. Saridakis and Y.-P. Wu, 2011 'Teleparallel' dark energy, Phys. Lett. B 704 384 [1109.1092]
34. C.-Q. Geng, C.-C. Lee and E.N. Saridakis, 2012 Observational constraints on teleparallel dark energy J. Cosmol. Astropart. Phys. JCAP01(2012)002 [1110.0913]
35. H. Wei, 2012 Dynamics of teleparallel dark energy, Phys. Lett. B 712 430 [1109.6107]
36. C. Xu, E.N. Saridakis and G. Leon, 2012 Phase-space analysis of teleparallel dark energy J. Cosmol. Astropart. Phys. JCAP07(2012)005 [1202.3781]
37. J.-A. Gu, C.-C. Lee and C.-Q. Geng, Tracker teleparallel dark energy with purely non-minimal coupling to gravity, [1204.4048]
38. R. Ferraro and F. Fiorini, 2007 Modified teleparallel gravity: inflation without inflaton, Phys. Rev. D 75 084031 [gr-qc/0610067]
39. R. Ferraro and F. Fiorini, 2008 On Born-Infeld gravity in Weitzenbock spacetime, Phys. Rev. D 78 124019 [0812.1981]
40. G.R. Bengochea and R. Ferraro, 2009 Dark torsion as the cosmic speed-up, Phys. Rev. D 79 124019 [0812.1205]
41. E.V. Linder, 2010 Einstein's other gravity and the acceleration of the universe, Phys. Rev. D 81 127301 [Erratum ibid D 82 (2010) 109902] [1005.3039]
42. K. Bamba, C.-Q. Geng and C.-C. Lee, Comment on 'Einstein's other gravity and the acceleration of the universe, [1008.4036]
43. P. Wu and H.W. Yu, 2011 f(T) models with phantom divide line crossing, Eur. Phys. J. C 71 1552 [1008.3669]
44. K. Bamba, C.-Q. Geng, C.-C. Lee and L.-W. Luo, 2011 Equation of state for dark energy in f(T) gravity J. Cosmol. Astropart. Phys. JCAP01(2011)021 [1011.0508]
45. P.P. Kronberg, 1994 Extragalactic magnetic fields, Rept. Prog. Phys. 57 325
46. D. Grasso and H.R. Rubinstein, 2001 Magnetic fields in the early universe, Phys. Rept. 348 163 [astro-ph/0009061]
47. C. Carilli and G. Taylor, 2002 Cluster magnetic fields, Ann. Rev. Astron. Astrophys. 40 319 [astro-ph/0110655]
48. L.M. Widrow, 2002 Origin of galactic and extragalactic magnetic fields, Rev. Mod. Phys. 74 775 [astro-ph/0207240]
49. M. Giovannini, 2004 The magnetized universe, Int. J. Mod. Phys. D 13 391 [astro-ph/0312614]
50. M. Giovannini, 2005 Theoretical tools for the physics of CMB anisotropies, Int. J. Mod. Phys. D 14 363 [astro-ph/0412601] (Pubitemid 40900746)
51. Magnetic fields, strings and cosmology Lect. Notes Phys. 737 2008 863 [astro-ph/0612378]
52. A. Kandus, K.E. Kunze and C.G. Tsagas, 2011 Primordial magnetogenesis, Phys. Rept. 505 1 [1007.3891]
53. L. Biermann and A. Schlüter, 1951 Cosmic radiation and cosmic magnetic fields. II. Origin of cosmic magnetic fields, Phys. Rev. 82 863
54. E.S. Weibel, 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution, Phys. Rev. Lett. 2 83
55. J.M. Quashnock, A. Loeb and D.N. Spergel, 1989 Magnetic field generation during the cosmological QCD phase transition, Astrophys. J. 344 L49
56. G. Baym, D. Bödeker and L.D. McLerran, 1996 Magnetic fields produced by phase transition bubbles in the electroweak phase transition, Phys. Rev. D 53 662 [hep-ph/9507429]
57. D. Boyanovsky, H.J. de Vega and M. Simionato, 2003 Large scale magnetogenesis from a non-equilibrium phase transition in the radiation dominated era, Phys. Rev. D 67 123505 [hep-ph/0211022] (Pubitemid 44652472)
58. D. Boyanovsky, M. Simionato and H.J. de Vega, 2003 Magnetic field generation from non-equilibrium phase transitions, Phys. Rev. D 67 023502 [hep-ph/0208272] (Pubitemid 44796914)
59. R. Durrer and C. Caprini, 2003 Primordial magnetic fields and causality J. Cosmol. Astropart. Phys. JCAP11(2003)010 [astro-ph/0305059]
60. T. Kahniashvili, A.G. Tevzadze and B. Ratra, 2011 Phase transition generated cosmological magnetic field at large scales, Astrophys. J. 726 78 [0907.0197]
61. Z. Berezhiani and A.D. Dolgov, 2004 Generation of large scale magnetic fields at recombination epoch, Astropart. Phys. 21 59 [astro-ph/0305595] (Pubitemid 38457857)
62. S. Matarrese, S. Mollerach, A. Notari and A. Riotto, 2005 Large-scale magnetic fields from density perturbations, Phys. Rev. D 71 043502 [astro-ph/0410687]
63. K. Takahashi, K. Ichiki, H. Ohno and H. Hanayama, 2005 Magnetic field generation from cosmological perturbations, Phys. Rev. Lett. 95 121301 [astro-ph/0502283] (Pubitemid 41505640)
64. K. Ichiki, K. Takahashi, H. Ohno, H. Hanayama and N. Sugiyama, 2006 Cosmological magnetic field: a fossil of density perturbations in the early universe, Science 311 827 [astro-ph/0603631] (Pubitemid 43228841)
65. E.R. Siegel and J.N. Fry, 2006 Cosmological structure formation creates large-scale magnetic fields, Astrophys. J. 651 627 [astro-ph/0604526] (Pubitemid 44973096)
66. T. Kobayashi, R. Maartens, T. Shiromizu and K. Takahashi, 2007 Cosmological magnetic fields from nonlinear effects, Phys. Rev. D 75 103501 [astro-ph/0701596]
67. K.E. Kunze, 2008 Primordial magnetic fields and nonlinear electrodynamics, Phys. Rev. D 77 023530 [0710.2435]
68. L. Campanelli, P. Cea, G. Fogli and L. Tedesco, 2008 Inflation-produced magnetic fields in nonlinear electrodynamics, Phys. Rev. D 77 043001 [0710.2993]
69. S. Maeda, S. Kitagawa, T. Kobayashi and T. Shiromizu, 2009 Primordial magnetic fields from second-order cosmological perturbations: tight coupling approximation, Class. Quant. Grav. 26 135014 [0805.0169]
70. E. Fenu, C. Pitrou and R. Maartens, 2011 The seed magnetic field generated during recombination, Mon. Not. Roy. Astron. Soc. 414 2354 [1012.2958]
71. E.N. Parker, 1971 The generation of magnetic fields in astrophysical bodies. II. The galactic field, Astrophys. J. 163 255
72. E.N. Parker, 1979 Cosmical magnetic fields (Clarendon, Oxford U.K.)
73. Ya.B. Zel'dovich, A.A. Ruzmaikin and D.D. Sokoloff, 1983 Magnetic fields in astrophysics, Gordon and Breach, New York U.S.A.
74. M.S. Turner and L.M. Widrow, 1988 Inflation produced, large scale magnetic fields, Phys. Rev. D 37 2743
75. I. Drummond and S. Hathrell, 1980 QED vacuum polarization in a background gravitational field and its effect on the velocity of photons, Phys. Rev. D 22 343
76. F.D. Mazzitelli and F.M. Spedalieri, 1995 Scalar electrodynamics and primordial magnetic fields, Phys. Rev. D 52 6694 [astro-ph/9505140]
77. G. Lambiase and A. Prasanna, 2004 Gauge invariant wave equations in curved space-times and primordial magnetic fields, Phys. Rev. D 70 063502 [gr-qc/0407071] (Pubitemid 44947278)
78. K. Bamba and S.D. Odintsov, 2008 Inflation and late-time cosmic acceleration in non-minimal Maxwell-F(R) gravity and the generation of large-scale magnetic fields J. Cosmol. Astropart. Phys. JCAP04(2008)024 [0801.0954]
79. K. Bamba, S. Nojiri and S.D. Odintsov, 2008 Inflationary cosmology and the late-time accelerated expansion of the universe in non-minimal Yang-Mills-F(R) gravity and non-minimal vector-F(R) gravity, Phys. Rev. D 77 123532 [0803.3384]
80. K. Bamba and S. Nojiri, Cosmology in non-minimal Yang-Mills/Maxwell theory, [0811.0150]
81. 2 models, Phys. Rev. D 77 123002 [0802.2630]
82. G. Lambiase, S. Mohanty and G. Scarpetta, 2008 Magnetic field amplification in f(R) theories of gravity J. Cosmol. Astropart. Phys. JCAP07(2008)019
83. K.E. Kunze, 2010 Large scale magnetic fields from gravitationally coupled electrodynamics, Phys. Rev. D 81 043526 [0911.1101]
84. J. Beltran Jimenez and A.L. Maroto, 2010 Dark energy, non-minimal couplings and the origin of cosmic magnetic fields J. Cosmol. Astropart. Phys. JCAP12(2010)025 [1010.4513]
85. L. Parker, 1968 Particle creation in expanding universes, Phys. Rev. Lett. 21 562
86. C.G. Tsagas, 2005 Electromagnetic fields in curved spacetimes, Class. Quant. Grav. 22 393 [gr-qc/0407080] (Pubitemid 40166954)
87. C.G. Tsagas and A. Kandus, 2005 Superadiabatic-type magnetic amplification in conventional cosmology, Phys. Rev. D 71 123506 [astro-ph/0504089]
88. J.D. Barrow and C.G. Tsagas, 2008 Slow decay of magnetic fields in open Friedmann universes, Phys. Rev. D 77 107302 [Erratum ibid D 77 (2008) 109904] [0803.0660]
89. J.D. Barrow and C.G. Tsagas, 2011 Cosmological magnetic field survival, Mon. Not. Roy. Astron. Soc. 414 512 [1101.2390]
90. A.L. Maroto, 2001 Primordial magnetic fields from metric perturbations, Phys. Rev. D 64 083006 [hep-ph/0008288]. (Pubitemid 33804079)
91. V. Demozzi, V. Mukhanov and H. Rubinstein, 2009 Magnetic fields from inflation? J. Cosmol. Astropart. Phys. JCAP08(2009)025 [0907.1030]
92. S. Kanno, J. Soda and M.-A. Watanabe, 2009 Cosmological magnetic fields from inflation and backreaction J. Cosmol. Astropart. Phys. JCAP12(2009)009 [0908.3509]
93. T. Suyama and J. Yokoyama, 2012 Metric perturbation from inflationary magnetic field and generic bound on inflation models, Phys. Rev. D 86 023512 [1204.3976]
94. T. Fujita and S. Mukohyama, 2012 Universal upper limit on inflation energy scale from cosmic magnetic field J. Cosmol. Astropart. Phys. JCAP10(2012)034 [1205.5031]
95. B. Ratra, 1992 Cosmological 'seed' magnetic field from inflation, Astrophys. J. 391 L1
96. D. Lemoine and M. Lemoine, 1995 Primordial magnetic fields in string cosmology, Phys. Rev. D 52 1955
97. M. Gasperini, M. Giovannini and G. Veneziano, 1995 Primordial magnetic fields from string cosmology, Phys. Rev. Lett. 75 3796 [hep-th/9504083]
98. K. Bamba and J. Yokoyama, 2004 Large scale magnetic fields from inflation in dilaton electromagnetism, Phys. Rev. D 69 043507 [astro-ph/0310824] (Pubitemid 44643173)
99. K. Bamba and J. Yokoyama, 2004 Large-scale magnetic fields from dilaton inflation in noncommutative spacetime, Phys. Rev. D 70 083508 [hep-ph/0409237] (Pubitemid 44947541)
100. J. Martin and J. Yokoyama, 2008 Generation of large-scale magnetic fields in single-field inflation J. Cosmol. Astropart. Phys. JCAP01(2008)025 [0711.4307]
101. K. Bamba and M. Sasaki, 2007 Large-scale magnetic fields in the inflationary universe J. Cosmol. Astropart. Phys. JCAP02(2007)030 [astro-ph/0611701]
102. K. Bamba, 2007 The interrelation between the generation of large-scale electric fields and that of large-scale magnetic fields during inflation J. Cosmol. Astropart. Phys. JCAP10(2007)015 [0710.1906]
103. K. Bamba, N. Ohta and S. Tsujikawa, 2008 Generic estimates for magnetic fields generated during inflation including Dirac-Born-Infeld theories, Phys. Rev. D 78 043524 [0805.3862]
104. K. Bamba, C. Geng and S. Ho, 2008 Large-scale magnetic fields from inflation due to Chern-Simons-like effective interaction J. Cosmol. Astropart. Phys. JCAP11(2008)013 [0806.1856]
105. K. Bamba, C. Geng, S. Ho and W. Kao, 2012 Large-scale magnetic fields from inflation due to a CPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields, Eur. Phys. J. C 72 1978 [1108.0151]
106. S.-H. Ho, W. Kao, K. Bamba and C. Geng, Cosmological birefringence due to CPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields, [1008.0486]
107. M. Giovannini, 2001 On the variation of the gauge couplings during inflation, Phys. Rev. D 64 061301 [astro-ph/0104290] (Pubitemid 33794480)
108. M. Giovannini, 2008 Magnetogenesis, spectator fields and CMB signatures, Phys. Lett. B 659 661 [0711.3273]
109. M. Giovannini, 2010 Electric-magnetic duality and the conditions of inflationary magnetogenesis J. Cosmol. Astropart. Phys. JCAP04(2010)003 [0911.0896]
110. E.W. Kolb and M.S. Turner, 1990 The early universe, Addison-Wesley, Redwood City U.S.A.
111. HST collaboration, W. Freedman et al., 2001 Final results from the Hubble Space Telescope key project to measure the Hubble constant, Astrophys. J. 553 47 [astro-ph/0012376]
112. A.G. Riess et al., 2009 A redetermination of the Hubble constant with the Hubble Space Telescope from a differential distance ladder, Astrophys. J. 699 539 [0905.0695]
113. V. Rubakov, M. Sazhin and A. Veryaskin, 1982 Graviton creation in the inflationary universe and the grand unification scale, Phys. Lett. B 115 189
114. L. Abbott and M.B. Wise, 1984 Constraints on generalized inflationary cosmologies, Nucl. Phys. B 244 541
115. K. Subramanian and J.D. Barrow, 1998 Microwave background signals from tangled magnetic fields, Phys. Rev. Lett. 81 3575 [astro-ph/9803261]
116. T.R. Seshadri and K. Subramanian, 2001 CMBR polarization signals from tangled magnetic fields, Phys. Rev. Lett. 87 101301 [astro-ph/0012056]
117. K. Subramanian and J.D. Barrow, 2002 Small-scale microwave background anisotropies due to tangled primordial magnetic fields, Mon. Not. Roy. Astron. Soc. 335 L57 [astro-ph/0205312]
118. K. Subramanian, T.R. Seshadri and J.D. Barrow, 2003 Small-scale CMB polarization anisotropies due to tangled primordial magnetic fields, Mon. Not. Roy. Astron. Soc. 344 L31 [astro-ph/0303014] (Pubitemid 37256522)
119. H. Tashiro, N. Sugiyama and R. Banerjee, 2006 Nonlinear evolution of cosmic magnetic fields and cosmic microwave background anisotropies, Phys. Rev. D 73 023002 [astro-ph/0509220]
120. D.G. Yamazaki, K. Ichiki, T. Kajino and G.J. Mathews, 2008 Effects of a primordial magnetic field on low and high multipoles of the CMB, Phys. Rev. D 77 043005 [0801.2572]
121. T. Kahniashvili, Y. Maravin and A. Kosowsky, 2009 Faraday rotation limits on a primordial magnetic field from Wilkinson Microwave Anisotropy Probe five-year data, Phys. Rev. D 80 023009 [0806.1876]
122. D.G. Yamazaki, K. Ichiki, T. Kajino and G.J. Mathews, 2010 New constraints on the primordial magnetic field, Phys. Rev. D 81 023008 [1001.2012]
123. J.R. Shaw and A. Lewis, 2012 Constraining primordial magnetism, Phys. Rev. D 86 043510 [1006.4242]
124. P. Trivedi, K. Subramanian and T. Seshadri, 2010 Primordial magnetic field limits from cosmic microwave background bispectrum of magnetic passive scalar modes, Phys. Rev. D 82 123006 [1009.2724]
125. M. Shiraishi, D. Nitta, S. Yokoyama, K. Ichiki and K. Takahashi, 2010 Cosmic microwave background bispectrum of vector modes induced from primordial magnetic fields, Phys. Rev. D 82 121302 [Erratum ibid D 83 (2011) 029901] [1009.3632]
126. M. Giovannini and K.E. Kunze, CMB polarization induced by stochastic magnetic fields, [0804.2238]
127. J.D. Barrow, P.G. Ferreira and J. Silk, 1997 Constraints on a primordial magnetic field, Phys. Rev. Lett. 78 3610 [astro-ph/9701063]
128. D.G. Yamazaki, K. Ichiki, T. Kajino and G.J. Mathews, 2008 Constraints on the primordial magnetic field from σ8, Phys. Rev. D 78 123001 [0811.2221]
129. D.G. Yamazaki, K. Ichiki, T. Kajino and G.J. Mathews, 2010 Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameter σ8, Phys. Rev. D 81 103519 [1005.1638]
130. S. Wang, 2010 New primordial-magnetic-field limit from the latest LIGO S-5 data, Phys. Rev. D 81 023002 [0810.5620]
131. H. Tashiro, K. Takahashi and K. Ichiki, Primordial magnetic fields with X-ray and S-Z cluster survey, [1010.4407]
132. K. Bamba, 2007 Property of the spectrum of large-scale magnetic fields from inflation, Phys. Rev. D 75 083516 [astro-ph/0703647].
133. D. Grasso and H.R. Rubinstein, 1996 Revisiting nucleosynthesis constraints on primordial magnetic fields, Phys. Lett. B 379 73 [astro-ph/9602055]
134. B.-L. Cheng, A.V. Olinto, D.N. Schramm and J.W. Truran, 1996 Constraints on the strength of primordial magnetic fields from big bang nucleosynthesis revisited, Phys. Rev. D 54 4714 [astro-ph/9606163]
135. C. Caprini, R. Durrer and T. Kahniashvili, 2004 The cosmic microwave background and helical magnetic fields: the tensor mode, Phys. Rev. D 69 063006 [astro-ph/0304556] (Pubitemid 44652784)
136. T. Kahniashvili and B. Ratra, 2005 Effects of cosmological magnetic helicity on the cosmic microwave background, Phys. Rev. D 71 103006 [astro-ph/0503709] (Pubitemid 44643227)
137. T. Kahniashvili, 2006 Effects of primordial helicity on CMB, New Astron. Rev. 50 1015 [astro-ph/0605440] (Pubitemid 44801313)
138. J.R. Kristiansen and P.G. Ferreira, 2008 Constraining primordial magnetic fields with CMB polarization experiments, Phys. Rev. D 77 123004 [0803.3210]
139. Planck science team homepage, http://www.sciops.esa.int/index.php? project=PLANCK
140. Planck, the scientific programme bluebook, http://www.rssd.esa.int/SA/ PLANCK/docs/Bluebook-ESA-SCI20051-V2.pdf
141. QUIET: Q/U Imaging ExperimenT webpage, http://quiet.uchicago.edu/index. php
142. QUIET collaboration, D. Samtleben, 2007 Measuring the Cosmic Microwave Background Radiation (CMBR) polarization with QUIET, Nuovo Cim. B 122 1353 [0802.2657]
143. B-Pol: a B-polarization satellite proposal for detecting primordial gravitational waves from inflation webpage, http://www.b-pol.org/index.php
144. LiteBIRD: Lite (light) satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection webpage, http://cmbpol.kek.jp/litebird/