Cosmological electromagnetic fields due to gravitational wave perturbations

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 62, Issue 10, 2000, Pages 1-5

  Marklund, Mattias ^a,b,c   Dunsby, Peter K S ^b   Brodin, Gert ^d  

^a SWEDISH DEFENCE RESEARCH AGENCY   (Sweden)

^b UNIVERSITY OF CAPE TOWN   (South Africa)

^c CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^d UMEÅ UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044382214     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.62.101501     Document Type: Article

References (49)

1. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
2. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
3. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
4. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
5. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
6. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
7. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
8. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
9. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
10. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
11. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
12. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
13. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
14. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
15. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
16. H. Stephani, General Relativity (Cambridge University Press, Cambridge, England, 1982); B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960); F. I. Cooperstock, ibid. 47, 173 (1968); Ya. B. Zeldovich, Zh. Eksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)]; U. N. Gerlach, Phys. Rev. Lett. 32, 1023 (1974); V. I. Denisov, Zh. Eksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 47, 209 (1978)]; L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 2; M. Demiański, Relativistic Astrophysics (Pergamon, New York, 1985), pp. 256-257; G. A. Lupanov, Zh. Eksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)]; V. B. Braginskiǐ et al., ibid. 65, 1729 (1973) [38, 865 (1974)]; L. P. Grishchuk and M. V. Sazhin, ibid. 68, 1569 (1975) [41, 787 (1976)].
17. D. Macdonald and K. S. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982); G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999); M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000); Yu. G. Ignat'ev, Phys. Lett. A 230, 171 (1997); R. Bingham et al., Phys. Scr. T75, 61 (1998); J. Daniel and T. Tajima, Phys. Rev. D 55, 5193 (1997).
18. D. Macdonald and K. S. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982); G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999); M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000); Yu. G. Ignat'ev, Phys. Lett. A 230, 171 (1997); R. Bingham et al., Phys. Scr. T75, 61 (1998); J. Daniel and T. Tajima, Phys. Rev. D 55, 5193 (1997).
19. D. Macdonald and K. S. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982); G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999); M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000); Yu. G. Ignat'ev, Phys. Lett. A 230, 171 (1997); R. Bingham et al., Phys. Scr. T75, 61 (1998); J. Daniel and T. Tajima, Phys. Rev. D 55, 5193 (1997).
20. D. Macdonald and K. S. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982); G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999); M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000); Yu. G. Ignat'ev, Phys. Lett. A 230, 171 (1997); R. Bingham et al., Phys. Scr. T75, 61 (1998); J. Daniel and T. Tajima, Phys. Rev. D 55, 5193 (1997).
21. D. Macdonald and K. S. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982); G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999); M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000); Yu. G. Ignat'ev, Phys. Lett. A 230, 171 (1997); R. Bingham et al., Phys. Scr. T75, 61 (1998); J. Daniel and T. Tajima, Phys. Rev. D 55, 5193 (1997).
22. D. Macdonald and K. S. Thorne, Mon. Not. R. Astron. Soc. 198, 345 (1982); G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999); M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000); Yu. G. Ignat'ev, Phys. Lett. A 230, 171 (1997); R. Bingham et al., Phys. Scr. T75, 61 (1998); J. Daniel and T. Tajima, Phys. Rev. D 55, 5193 (1997).
23. E. Battaner and H. Lesch, "On the Physics of Primordial Magnetic Fields," astro-ph/0003370 (2000).
24. R. Brustein and D. H. Oaknin, Phys. Rev. D 60, 023508 (1999); M. Giovannini and M. Shaposhnikov, ibid, (to be published), hep-ph/0004269.
25. R. Brustein and D. H. Oaknin, Phys. Rev. D 60, 023508 (1999); M. Giovannini and M. Shaposhnikov, ibid, (to be published), hep-ph/0004269.
26. M. Gaperini, M. Giovannini, and G. Veneziano, Phys. Rev. Lett. 75, 3796 (1995).
27. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
28. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
29. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
30. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
31. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
32. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
33. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
34. T. V. Ruzmaikina and A. A. Ruzmaikin, Astron. Zh. 47, 1206 (1971) [Sov. Astron. 14, 963 (1971)]; I. Wasserman, Astrophys. J. 224, 337 (1978); E. Kim, A. Olinto, and R. Rosner, ibid. 468, 28 (1996); E. Battaner, E. Florido, and J. Jiménez-Vicente, Astron. Astrophys. 326, 13 (1997); K. Jedamzik, V. Katalinic, and A. Olinto, Phys. Rev. D 57, 3264 (1998); C. G. Tsagas and R. Maartens, ibid. 61, 083519 (2000); S. Hobbs and P. K. S. Dunsby, "Dynamical systems analysis of magnetised density perturbations," gr-qc/0007010 (2000).
35. C. G. Tsagas and J. D. Barrow, Class. Quantum Grav. 15, 3523 (1998).
36. G. F. R. Ellis and M. Bruni, Phys. Rev. D 40, 1804 (1989).
37. S. W. Hawking, Astrophys. J. 145, 544 (1966).
38. P. K. S. Dunsby, B. A. C. C. Bassett, and G. F. R. Ellis, Class. Quantum Grav. 14, 1215 (1997).
39. Although this in principle breaks the homogeneity and isotropy of the FRW spacetime, a weak magnetic test field can be shown to be consistent in such a background provided the spatial variations it generates are negligible.
40. G. F. R. Ellis and H. van Elst, Cosmological models (Cargèse lectures 1998), in Theoretical and Observational Cosmology, edited by M. Lachièze-Rey (Kluwer, Dordrecht, 1999), p. 1.
41. R. Maartens, Phys. Rev. D 55, 463 (1997).
42. J. Bardeen, Phys. Rev. D 22, 1882 (1980).
43. a.
44. E. R. Harrison, Rev. Mod. Phys. 39, 862 (1967).
45. J. Wainwright and G. F. R. Ellis, Dynamical Systems in Cosmology (Cambridge University Press, Cambridge, England, 1997).
46. G. F. R. Ellis, Relativistic Cosmology, in Cargèse Lectures in Physics, Volume 6, edited by E. Schatzmann (Gordon and Breach, New York, 1973).
47. W. Stoeger, M. Araujo, and T. Gebbie, Astrophys. J. 476, 435 (1997); 522, 559 (1999).
48. W. Stoeger, M. Araujo, and T. Gebbie, Astrophys. J. 476, 435 (1997); 522, 559 (1999).
49. P. K. S. Dunsby, M. Marklund, and G. Brodin, Electromagnetic Fields in the Early Universe (in preparation).