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Advances in Astronomy
Volume 2010 (2010), Article ID 380507, 28 pages
http://dx.doi.org/10.1155/2010/380507
Review Article

Cosmic Strings and Their Induced Non-Gaussianities in the Cosmic Microwave Background

Institute of Mathematics and Physics, Centre for Cosmology, Particle Physics and Phenomenology, Louvain University, 2 Chemin du Cyclotron, 348 Louvain-la-Neuve, Belgium

Received 15 January 2010; Accepted 27 May 2010

Academic Editor: Eiichiro Komatsu

Copyright © 2010 Christophe Ringeval. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. A. Kirzhnits and A. D. Linde, “Macroscopic consequences of the Weinberg model,” Physics Letters B, vol. 42, no. 4, pp. 471–474, 1972. View at Google Scholar · View at Scopus
  2. I. Y. Kobsarev, L. B. Okun, and Y. B. Zeldovich, “Spontaneus CP-violation and cosmology,” Physics Letters B, vol. 50, no. 3, pp. 340–342, 1974. View at Google Scholar · View at Scopus
  3. T. W. B. Kibble, “Topology of cosmic domains and strings,” Journal of Physics A, vol. 9, no. 8, pp. 1387–1398, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. M. B. Hindmarsh and T. W. B. Kibble, “Cosmic strings,” Reports on Progress in Physics, vol. 58, no. 5, pp. 477–562, 1995. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge University Press, Cambridge, UK, 2000.
  6. M. Sakellariadou, “Cosmic strings,” Lecture Notes in Physics, vol. 718, pp. 247–288, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Peter and J.-P. Uzan, Primordial Cosmology, Oxford Graduate Texts, Oxford University Press, Oxford, UK, 2009.
  8. S. Sarkar, “Big bang nucleosynthesis and physics beyond the standard model,” Reports on Progress in Physics, vol. 59, no. 12, pp. 1493–1609, 1996. View at Google Scholar · View at Scopus
  9. R. H. Cyburt, B. D. Fields, K. A. Olive, and E. Skillman, “New BBN limits on physics beyond the standard model from 4He,” Astroparticle Physics, vol. 23, no. 3, pp. 313–323, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. T. W. B. Kibble, G. Lazarides, and Q. Shafi, “Walls bounded by strings,” Physical Review D, vol. 26, no. 2, pp. 435–439, 1982. View at Publisher · View at Google Scholar · View at Scopus
  11. P. Langacker and S.-Y. Pi, “Magnetic monopoles in grand unified theories,” Physical Review Letters, vol. 45, no. 1, pp. 1–4, 1980. View at Publisher · View at Google Scholar · View at Scopus
  12. A. H. Guth, “Inflationary universe: a possible solution to the horizon and flatness problems,” Physical Review D, vol. 23, no. 2, pp. 347–356, 1981. View at Publisher · View at Google Scholar · View at Scopus
  13. A. A. Starobinsky, “A new type of isotropic cosmological models without singularity,” Physics Letters B, vol. 91, no. 1, pp. 99–102, 1980. View at Google Scholar · View at Scopus
  14. A. D. Linde, “A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems,” Physics Letters B, vol. 108, no. 6, pp. 389–393, 1982. View at Google Scholar · View at Scopus
  15. A. A. Starobinsky, “Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations,” Physics Letters B, vol. 117, no. 3-4, pp. 175–178, 1982. View at Google Scholar · View at Scopus
  16. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberge, “Theory of cosmological perturbations, part I: classical perturbations,” Physics Reports, vol. 215, no. 5-6, pp. 203–256, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberge, “Theory of cosmological perturbations, part II: quantum perturbations,” Physics Reports, vol. 215, no. 5-6, pp. 257–295, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberge, “Theory of cosmological perturbations, part III: extensions,” Physics Reports, vol. 215, no. 5-6, pp. 296–333, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. Martin and C. Ringeval, “Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data,” Journal of Cosmology and Astroparticle Physics, vol. 2006, no. 8, article 9, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. P. P. Avelino, C. J. A. P. Martins, and E. P. S. Shellard, “Effects of inflation on a cosmic string loop population,” Physical Review D, vol. 76, no. 8, Article ID 083510, 7 pages, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. R. Jeannerot, J. Rocher, and M. Sakellariadou, “How generic is cosmic string formation in supersymmetric grand unified theories,” Physical Review D, vol. 68, no. 10, Article ID 103514, 20 pages, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Rocher and M. Sakellariadou, “D-term inflation, cosmic strings, and consistency with cosmic microwave background measurements,” Physical Review Letters, vol. 94, no. 1, Article ID 011303, 2005. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Rocher and M. Sakellariadou, “D-term inflation in non-minimal supergravity,” Journal of Cosmology and Astroparticle Physics, no. 11, article 1, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. R. A. Battye, B. Garbrecht, and A. Moss, “Constraints on supersymmetric hybrid inflation models,” Journal of Cosmology and Astroparticle Physics, vol. 2006, no. 9, article 7, 2006. View at Publisher · View at Google Scholar · View at Scopus
  25. K. Becker, M. Becker, and J. H. Schwarz, String Theory and M-Theory: A Modern Introduction, Cambridge University Press, Cambridge, UK, 2007.
  26. G. Dvali and S.-H. H. Tye, “Brane inflation,” Physics Letters B, vol. 450, no. 1–3, pp. 72–82, 1999. View at Google Scholar · View at Scopus
  27. S. H. S. Alexander, “Inflation from DD¯ brane annihilation,” Physical Review D, vol. 65, no. 2, Article ID 023507, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. S. Kachru, R. Kallosh, A. Linde, J. Maldacena, L. McAllister, and S. P. Trivedi, “Towards inflation in string theory,” Journal of Cosmology and Astroparticle Physics, vol. 2003, no. 10, article 13, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. C. P. Burgess, M. Majumdar, D. Nolte, F. Quevedo, G. Rajesh, and R.-J. Zhang, “The inflationary brane-antibrane universe,” Journal of High Energy Physics, vol. 5, no. 7, article 47, 2001. View at Google Scholar · View at Scopus
  30. S. Sarangi and S.-H. Tye, “Cosmic string production towards the end of brane inflation,” Physics Letters B, vol. 536, no. 3-4, pp. 185–192, 2002. View at Publisher · View at Google Scholar · View at Scopus
  31. G. Dvali and A. Vilenkin, “Formation and evolution of cosmic D strings,” Journal of Cosmology and Astroparticle Physics, vol. 2004, no. 3, article 10, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. N. T. Jones, H. Stoica, and S.-H. H. Tye, “The production, spectrum and evolution of cosmic strings in brane inflation,” Physics Letters B, vol. 563, no. 1-2, pp. 6–14, 2003. View at Publisher · View at Google Scholar · View at Scopus
  33. A.-C. Davis and T. W. B. Kibble, “Fundamental cosmic strings,” Contemporary Physics, vol. 46, no. 5, pp. 313–322, 2005. View at Publisher · View at Google Scholar · View at Scopus
  34. E. J. Copeland and T. W. B. Kibble, “Cosmic strings and superstrings,” Proceedings of the Royal Society A, vol. 466, no. 2115, pp. 623–657, 2010. View at Publisher · View at Google Scholar · View at Scopus
  35. M. Sakellariadou, “Cosmic superstrings,” Philosophical Transactions of the Royal Society A, vol. 366, no. 1877, pp. 2881–2894, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  36. M. Sakellariadou, “Cosmic strings and cosmic superstrings,” Nuclear Physics B—Proceedings Supplements, vol. 192-193, pp. 68–90, 2009. View at Publisher · View at Google Scholar · View at Scopus
  37. F. R. Bouchet, D. P. Bennett, and A. Stebbins, “Patterns of the cosmic microwave background from evolving string networks,” Nature, vol. 335, no. 6189, pp. 410–414, 1988. View at Google Scholar
  38. B. Carter, “Duality relation between charged elastic strings and superconducting cosmic strings,” Physics Letters B, vol. 224, no. 1-2, pp. 61–66, 1989. View at Google Scholar
  39. R. Durrer, M. Kunz, and A. Melchiorri, “Cosmic structure formation with topological defects,” Physics Report, vol. 364, no. 1, pp. 1–81, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. R. Durrer, A. Gangui, and M. Sakellariadou, “Doppler peaks in the angular power spectrum of the cosmic microwave background: a fingerprint of topological defects,” Physical Review Letters, vol. 76, no. 4, pp. 579–582, 1996. View at Google Scholar · View at Scopus
  41. J. Magueijo, A. Albrecht, P. Ferreira, and D. Coulson, “The structure of Doppler peaks induced by active perturbations,” Physical Review D, vol. 54, no. 6, pp. 3727–3744, 1996. View at Google Scholar · View at Scopus
  42. A. Albrecht, R. A. Battye, and J. Robinson, “The case against scaling defect models of cosmic structure formation,” Physical Review Letters, vol. 79, no. 24, pp. 4736–4739, 1997. View at Google Scholar · View at Scopus
  43. D. N. Spergel, R. Bean, and R. Bean, “Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: implications for cosmology,” Astrophysical Journal, Supplement Series, vol. 170, no. 2, pp. 377–408, 2007. View at Publisher · View at Google Scholar · View at Scopus
  44. E. Komatsu, J. Dunkley, and J. Dunkley, “Five-year wilkinson microwave anisotropy probe observations: cosmological interpretation,” Astrophysical Journal, Supplement Series, vol. 180, no. 2, pp. 330–376, 2009. View at Publisher · View at Google Scholar · View at Scopus
  45. F. R. Bouchet, P. Peter, A. Riazuelo, and M. Sakellariadou, “Evidence against or for topological defects in the BOOMERanG data?” Physical Review D, vol. 65, no. 2, Article ID 021301, 4 pages, 2001. View at Publisher · View at Google Scholar · View at Scopus
  46. A. A. Fraisse, “Limits on defects formation and hybrid inflationary models with three-year WMAP observations,” Journal of Cosmology and Astroparticle Physics, vol. 2007, no. 3, article 8, 2007. View at Publisher · View at Google Scholar · View at Scopus
  47. N. Bevis, M. Hindmarsh, M. Kunz, and J. Urrestilla, “Fitting cosmic microwave background data with cosmic strings and inflation,” Physical Review Letters, vol. 100, no. 2, Article ID 021301, 2008. View at Publisher · View at Google Scholar · View at Scopus
  48. A. M. Gilbert and L. Perivolaropoulos, “Spectra and statistics of cosmic string perturbations on the microwave background: a Monte Carlo approach,” Astroparticle Physics, vol. 3, no. 3, pp. 283–294, 1995. View at Google Scholar · View at Scopus
  49. E. Jeong and G. F. Smoot, “The validity of the cosmic string pattern search with the cosmic microwave background,” Astrophysical Journal, vol. 661, no. 1, pp. L1–L4, 2007. View at Publisher · View at Google Scholar · View at Scopus
  50. S. Amsel, J. Berger, and R. H. Brandenberger, “Detecting cosmic strings in the CMB with the canny algorithm,” Journal of Cosmology and Astroparticle Physics, vol. 2008, no. 4, article 15, 2008. View at Publisher · View at Google Scholar
  51. A. Gangui, L. Pogosian, and S. Winitzki, “CMB bispectrum from active models of structure formation,” Physical Review D, vol. 64, no. 4, Article ID 043001, 7 pages, 2001. View at Publisher · View at Google Scholar · View at Scopus
  52. L. Pogosian and M. Wyman, “B-modes from cosmic strings,” Physical Review D, vol. 77, no. 8, Article ID 083509, 11 pages, 2008. View at Publisher · View at Google Scholar · View at Scopus
  53. J. R. Gott III, “Gravitational lensing effects of vacuum strings—exact solutions,” Astrophysical Journal, vol. 288, no. 8, pp. 422–427, 1985. View at Publisher · View at Google Scholar · View at Scopus
  54. N. Kaiser and A. Stebbins, “Microwave anisotropy due to cosmic strings,” Nature, vol. 310, no. 5976, pp. 391–393, 1984. View at Publisher · View at Google Scholar · View at Scopus
  55. E. Sefusatti and E. Komatsu, “The bispectrum of galaxies from high-redshift galaxy surveys: primordial non-Gaussianity and non-linear galaxy bias,” Physical Review D, vol. 76, no. 8, Article ID 083004, 17 pages, 2007. View at Publisher · View at Google Scholar · View at Scopus
  56. C. Pitrou, J.-P. Uzan, and F. Bernardeau, “Cosmic microwave background bispectrum on small angular scales,” Physical Review D, vol. 78, no. 6, Article ID 063526, 2008. View at Publisher · View at Google Scholar · View at Scopus
  57. D. Nitta, E. Komatsu, N. Bartolo, S. Matarrese, and A. Riotto, “CMB anisotropies at second order III: bispectrum from products of the first-order perturbations,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 5, article 14, 2009. View at Publisher · View at Google Scholar · View at Scopus
  58. L. Boubekeur, P. Creminelli, G. D'Amico, J. Norea, and F. Vernizzi, “Sachs-wolfe at second order: the CMB bispectrum on large angular scales,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 8, article 29, 2009. View at Publisher · View at Google Scholar · View at Scopus
  59. S. Weinberg, “Conceptual foundations of the unified theory of weak and electromagnetic interactions,” Reviews of Modern Physics, vol. 52, no. 3, pp. 515–523, 1980. View at Publisher · View at Google Scholar · View at Scopus
  60. A. J. Gill and R. J. Rivers, “Dynamics of vortex and monopole production by quench-induced phase separation,” Physical Review D, vol. 51, no. 12, pp. 6949–6958, 1995. View at Publisher · View at Google Scholar · View at Scopus
  61. G. Karra and R. J. Rivers, “Initial vortex densities after a temperature quench,” Physics Letters B, vol. 414, no. 1-2, pp. 28–33, 1997. View at Google Scholar · View at Scopus
  62. L. M. A. Bettencourt, T. S. Evans, and R. J. Rivers, “Winding number correlation functions and cosmic string formation,” Physical Review D, vol. 53, no. 2, pp. 668–680, 1996. View at Google Scholar · View at Scopus
  63. E. Kavoussanaki, R. Monaco, and R. J. Rivers, “Testing the kibble-zurek scenario with annular Josephson tunnel junctions,” Physical Review Letters, vol. 85, no. 16, pp. 3452–3455, 2000. View at Publisher · View at Google Scholar · View at Scopus
  64. N. K. Nielsen and P. Olesen, “Dynamical properties of superconducting cosmic strings,” Nuclear Physics B, vol. 291, pp. 829–846, 1987. View at Google Scholar · View at Scopus
  65. P. Peter, “Superconducting cosmic string: equation of state for spacelike and timelike current in the neutral limit,” Physical Review D, vol. 45, no. 4, pp. 1091–1102, 1992. View at Publisher · View at Google Scholar · View at Scopus
  66. C. Ringeval, “Equation of state of cosmic strings with fermionic current carriers,” Physical Review D, vol. 63, no. 6, Article ID 063508, 24 pages, 2001. View at Publisher · View at Google Scholar · View at Scopus
  67. A. Vilenkin, “Gravitational field of vacuum domain walls and strings,” Physical Review D, vol. 23, no. 4, pp. 852–857, 1981. View at Publisher · View at Google Scholar · View at Scopus
  68. L. M. A. Bettencourt and R. J. Rivers, “Interactions between U(1) cosmic strings: an analytical study,” Physical Review D, vol. 51, no. 4, pp. 1842–1853, 1995. View at Publisher · View at Google Scholar · View at Scopus
  69. N. D. Antunes, L. M. A. Bettencourt, and M. Hindmarsh, “Thermodynamics of cosmic string densities in U(1) scalar field theory,” Physical Review Letters, vol. 80, no. 5, pp. 908–911, 1998. View at Google Scholar · View at Scopus
  70. T. Vachaspati and A. Vilenkin, “Formation and evolution of cosmic strings,” Physical Review D, vol. 30, no. 10, pp. 2036–2045, 1984. View at Publisher · View at Google Scholar · View at Scopus
  71. M. Hindmarsh and A. Rajantie, “Phase transition dynamics in the hot Abelian Higgs model,” Physical Review D, vol. 64, no. 6, Article ID 065016, 13 pages, 2001. View at Publisher · View at Google Scholar · View at Scopus
  72. M. Donaire and A. Rajantie, “Heavy cosmic strings,” Physical Review D, vol. 73, no. 6, Article ID 063517, 4 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  73. A. Rajantie, “Super-horizon cosmic string correlations,” Physical Review D, vol. 79, no. 4, Article ID 043515, 2009. View at Publisher · View at Google Scholar · View at Scopus
  74. M. Sakellariadou and H. Stoica, “Dynamics of F/D networks: the role of bound states,” Journal of Cosmology and Astroparticle Physics, vol. 2008, no. 8, article 38, 2008. View at Publisher · View at Google Scholar · View at Scopus
  75. G. Vincent, N. D. Antunes, and M. Hindmarsh, “Numerical simulations of string networks in the Abelian-Higgs model,” Physical Review Letters, vol. 80, no. 11, pp. 2277–2280, 1998. View at Google Scholar · View at Scopus
  76. J. N. Moore, E. P. S. Shellard, and C. J. A. P. Martins, “Evolution of Abelian-Higgs string networks,” Physical Review D, vol. 65, no. 2, Article ID 023503, 19 pages, 2001. View at Publisher · View at Google Scholar · View at Scopus
  77. M. Hindmarsh, S. Stuckey, and N. Bevis, “Abelian Higgs cosmic strings: small-scale structure and loops,” Physical Review D, vol. 79, no. 12, Article ID 123504, 2009. View at Publisher · View at Google Scholar · View at Scopus
  78. R. L. Davis, “Goldstone bosons in string models of galaxy formation,” Physical Review D, vol. 32, no. 12, pp. 3172–3177, 1985. View at Publisher · View at Google Scholar · View at Scopus
  79. R. Durrer, M. Kunz, and A. Melchiorri, “Cosmic microwave background anisotropies from scaling seeds: global defect models,” Physical Review D, vol. 59, no. 12, Article ID 123005, 26 pages, 1999. View at Publisher · View at Google Scholar · View at Scopus
  80. M. Yamaguchi, “Scaling property of the global string in the radiation dominated universe,” Physical Review D, vol. 60, no. 10, Article ID 103511, 10 pages, 1999. View at Publisher · View at Google Scholar · View at Scopus
  81. M. Yamaguchi, J. Yokoyama, and M. Kawasaki, “Evolution of a global string network in a matter-dominated universe,” Physical Review D, vol. 61, no. 6, Article ID 061301, 5 pages, 2000. View at Publisher · View at Google Scholar · View at Scopus
  82. P. McGraw, “Evolution of a non-abelian cosmic string network,” Physical Review D, vol. 57, no. 6, pp. 3317–3339, 1998. View at Google Scholar · View at Scopus
  83. A. Vilenkin, “String-dominated universe,” Physical Review Letters, vol. 53, no. 10, pp. 1016–1018, 1984. View at Publisher · View at Google Scholar · View at Scopus
  84. G. Dvali and G. Senjanović, “Flavor changing strings and domain walls,” Physical Review Letters, vol. 72, no. 1, pp. 9–12, 1994. View at Publisher · View at Google Scholar · View at Scopus
  85. D. Spergel and U.-L. Pen, “Cosmology in a string-dominated universe,” Astrophysical Journal, vol. 491, no. 2, pp. L67–L71, 1997. View at Google Scholar · View at Scopus
  86. M. Bucher and D. Spergel, “Is the dark matter a solid?” Physical Review D, vol. 60, no. 4, Article ID 043505, 11 pages, 1999. View at Google Scholar · View at Scopus
  87. K. Hashimoto and D. Tong, “Reconnection of non-abelian cosmic strings,” Journal of Cosmology and Astroparticle Physics, vol. 2005, no. 9, article 4, pp. 53–72, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  88. M. Eto et al., “Universal reconnection of non-Abelian cosmic strings,” Physics Review Letters, vol. 98, no. 9, Article ID 091602, 4 pages, 2007. View at Publisher · View at Google Scholar
  89. M. Eto, Y. Isozumi, M. Nitta, K. Ohashi, and N. Sakai, “Solitons in the Higgs phase: The moduli matrix approach,” Journal of Physics A, vol. 39, no. 26, pp. R315–R392, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  90. M. Shifman and A. Yung, “Supersymmetric solitons and how they help us understand and non-abelian gauge theories,” Reviews of Modern Physics, vol. 79, no. 4, pp. 1139–1196, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  91. M. Kobayashi, Y. Kawaguchi, M. Nitta, and M. Ueda, “Collision dynamics and rung formation of non-Abelian vortices,” Physics Review Letters, vol. 103, no. 11, Article ID 115301, 4 pages, 2009. View at Publisher · View at Google Scholar
  92. T. Vachaspati and A. Achúcarro, “Semilocal cosmic strings,” Physical Review D, vol. 44, no. 10, pp. 3067–3071, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  93. A. Achúcarro, J. Borrill, and A. R. Liddle, “Formation rate of semilocal strings,” Physical Review Letters, vol. 82, no. 19, pp. 3742–3745, 1999. View at Google Scholar
  94. A. Achúcarro and T. Vachaspati, “Semilocal and electroweak strings,” Physics Report, vol. 327, no. 6, pp. 347–426, 2000. View at Publisher · View at Google Scholar
  95. M. Hindmarsh, “Existence and stability of semilocal strings,” Physical Review Letters, vol. 68, no. 9, pp. 1263–1266, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  96. X. Zhang, T. Huang, and R. H. Brandenberger, “Pion and η′ strings,” Physical Review D, vol. 58, no. 2, Article ID 027702, 3 pages, 1998. View at Publisher · View at Google Scholar
  97. A. P. Balachandran and S. Digal, “Topological string defect formation during the chiral phase transition,” International Journal of Modern Physics A, vol. 17, no. 8, pp. 1149–1158, 2002. View at Publisher · View at Google Scholar
  98. K. B. W. Buckley and A. R. Zhitnitsky, “Superconducting K strings in high density QCD,” Journal of High Energy Physics, vol. 6, no. 8, pp. 235–249, 2002. View at Google Scholar
  99. R. H. Brandenberger, B. Carter, and A.-C. Davis, “Microwave background constraints on decaying defects,” Physics Letters B, vol. 534, no. 1–4, pp. 1–7, 2002. View at Publisher · View at Google Scholar
  100. M. Nitta and N. Shiiki, “Non-Abelian global strings at chiral phase transition,” Physics Letters B, vol. 658, no. 4, pp. 143–147, 2008. View at Publisher · View at Google Scholar
  101. M. Eto, E. Nakano, and M. Nitta, “Non-Abelian global vortices,” Nuclear Physics B, vol. 821, no. 1-2, pp. 129–150, 2009. View at Publisher · View at Google Scholar
  102. E. Nakano, M. Nitta, and T. Matsuura, “Non-Abelian strings in hot or dense QCD,” Progress of Theoretical Physics Supplement, vol. 174, pp. 254–257, 2008. View at Publisher · View at Google Scholar
  103. M. Eto, M Nitta, and N. Yamamoto, “Instabilities of non-nbelian vortices in dense QCD,” Physical Review Letters, vol. 104, no. 16, Article ID 161601, 4 pages, 2010. View at Publisher · View at Google Scholar
  104. E. Babichev, “Global topological k-defects,” Physical Review D, vol. 74, no. 8, Article ID 085004, 7 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  105. E. Babichev, “Gauge k-vortices,” Physical Review D, vol. 77, no. 6, Article ID 065021, 2008. View at Publisher · View at Google Scholar
  106. S. Sarangi, “DBI global strings,” Journal of High Energy Physics, vol. 2008, no. 7, article 18, 2008. View at Publisher · View at Google Scholar
  107. E. Babichev, P. Brax, C. Caprini, J. Martin, and D. A. Steer, “Dirac Born Infeld (DBI) cosmic strings,” Journal of High Energy Physics, vol. 2009, no. 3, article 91, 2009. View at Publisher · View at Google Scholar
  108. E. Witten, “Superconducting strings,” Nuclear Physics B, vol. 249, no. 4, pp. 557–592, 1985. View at Google Scholar
  109. B. Carter, “Essentials of classical brane dynamics,” International Journal of Theoretical Physics, vol. 40, no. 12, pp. 2099–2130, 2001. View at Google Scholar
  110. R. L. Davis, “Semitopological solitons,” Physical Review D, vol. 38, no. 12, pp. 3722–3730, 1988. View at Publisher · View at Google Scholar
  111. R. Brandenberger, B. Carter, A.-C. Davis, and M. Trodden, “Cosmic vortons and particle physics constraints,” Physical Review D, vol. 54, no. 10, pp. 6059–6071, 1996. View at Google Scholar
  112. C. Ringeval, “Fermionic massive modes along cosmic strings,” Physical Review D, vol. 64, no. 12, Article ID 123505, 2001. View at Google Scholar
  113. B. Carter and X. Martin, “Dynamical instability criterion for circular (vorton) string loops,” Annals of Physics, vol. 227, no. 1, pp. 151–171, 1993. View at Google Scholar
  114. X. Martin, “Zones of dynamical instability for rotating string loops,” Physical Review D, vol. 50, no. 12, pp. 7479–7492, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  115. J. Polchinski, “Introduction to cosmic F- and D-strings,” in Lectures Given at NATO Advanced Study Institute and EC Summer School on String Theory: From Gauge Interactions to Cosmology, pp. 229–253, Cargese, France, June 2004.
  116. A.-C. Davis, P. Brax, and C. Van De Bruck, “Brane inflation and defect formation,” Philosophical Transactions of the Royal Society A, vol. 366, no. 1877, pp. 2833–2842, 2008. View at Publisher · View at Google Scholar · View at PubMed
  117. E. Witten, “Cosmic superstrings,” Physics Letters B, vol. 153, no. 4-5, pp. 243–246, 1985. View at Google Scholar
  118. L. Lorenz, J. Martin, and C. Ringeval, “Constraints on kinetically modified inflation from WMAP5,” Physical Review D, vol. 78, no. 6, Article ID 063543, 2008. View at Publisher · View at Google Scholar
  119. S. B. Giddings, S. Kachru, and J. Polchinski, “Hierarchies from fluxes in string compactifications,” Physical Review D, vol. 66, no. 10, Article ID 106006, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  120. I. R. Klebanov and M. J. Strassler, “Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities,” Journal of High Energy Physics, vol. 4, no. 8, pp. 21–35, 2000. View at Google Scholar
  121. L. Lorenz, J. Martin, and C. Ringeval, “Brane inflation and the WMAP data: a Bayesian analysis,” Journal of Cosmology and Astroparticle Physics, vol. 2008, no. 4, article 1, 2008. View at Publisher · View at Google Scholar
  122. H. Firouzjahi and S.-H. H. Tye, “Brane inflation and cosmic string tension in superstring theory,” Journal of Cosmology and Astroparticle Physics, vol. 2005, no. 3, pp. 115–131, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  123. S. S. Gubser, C. P. Herzog, and I. R. Klebanov, “Symmetry breaking and axionic strings in the warped deformed conifold,” Journal of High Energy Physics, vol. 8, no. 9, pp. 795–820, 2004. View at Google Scholar
  124. H. Firouzjahi, L. Leblond, and S.-H. H. Tye, “The (p,q) string tension in a warped deformed conifold,” Journal of High Energy Physics, vol. 2006, no. 5, article 47, 2006. View at Google Scholar
  125. M. G. Jackson, “A note on Cosmic (p,q,r) strings,” Physical Review D, vol. 75, no. 8, Article ID 087301, 2007. View at Publisher · View at Google Scholar
  126. E. J. Copeland, T. W. B. Kibble, and D. A. Steer, “Constraints on string networks with junctions,” Physical Review D, vol. 75, no. 6, Article ID 065024, 12 pages, 2007. View at Publisher · View at Google Scholar
  127. R. J. Rivers and D. A. Steer, “Statistical mechanics of strings with Y-junctions,” Physical Review D, vol. 78, no. 2, Article ID 023521, 13 pages, 2008. View at Publisher · View at Google Scholar
  128. N. Bevis, E. J. Copeland, P.-Y. Martin et al., “Evolution and stability of cosmic string loops with Y-junctions,” Physical Review D, vol. 80, no. 12, Article ID 125030, 14 pages, 2009. View at Publisher · View at Google Scholar
  129. P. M. Saffin, “A practical model for cosmic (p,q) superstrings,” Journal of High Energy Physics, vol. 2005, no. 9, pp. 283–295, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  130. I. Cho, Y. Kim, and B. Kyae, “DF-strings from D3D¯3 as cosmic strings,” Journal of High Energy Physics, vol. 2006, no. 4, article 12, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  131. M. Hindmarsh and P. M. Saffin, “Scaling in a SU(2)/3 model of cosmic superstring networks,” Journal of High Energy Physics, vol. 2006, no. 8, article 66, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  132. A. Rajantie, M. Sakellariadou, and H. Stoica, “Numerical experiments with p F- and p D-strings: the formation of (p,q) bound states,” Journal of Cosmology and Astroparticle Physics, vol. 2007, no. 11, article 21, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  133. B. Carter, “Stability and characteristic propagation speeds in superconducting cosmic and other string models,” Physics Letters B, vol. 228, no. 4, pp. 466–470, 1989. View at Google Scholar
  134. B. Carter, “Outer curvature and conformal geometry of an imbedding,” Journal of Geometry and Physics, vol. 8, pp. 53–88, 1992. View at Google Scholar
  135. R. M. Wald, General Relativity, University of Chicago Press, Chicago, Ill, USA, 1984.
  136. B. Carter, M. Sakellariadou, and X. Martin, “Cosmological expansion and thermodynamic mechanisms in cosmic string dynamics,” Physical Review D, vol. 50, no. 2, pp. 682–699, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  137. B. Carter, “Integrable equation of state for noisy cosmic string,” Physical Review D, vol. 41, no. 12, pp. 3869–3872, 1990. View at Publisher · View at Google Scholar
  138. B. Carter, “Transonic elastic model for wiggly Goto-Nambu string,” Physical Review Letters, vol. 74, no. 16, pp. 3098–3101, 1995. View at Publisher · View at Google Scholar
  139. B. Carter and D. A. Steer, “Symplectic structure for elastic and chiral conducting cosmic string models,” Physical Review D, vol. 69, no. 12, Article ID 125002, 9 pages, 2004. View at Publisher · View at Google Scholar
  140. B. Carter and P. Peter, “Dynamics and integrability property of the chiral string model,” Physics Letters B, vol. 466, no. 1, pp. 41–49, 1999. View at Google Scholar
  141. T. Goto, “Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model,” Progress of Theoretical Physics, vol. 46, no. 5, pp. 1560–1569, 1971. View at Google Scholar
  142. D. P. Bennett and F. R. Bouchet, “Cosmic-string evolution,” Physical Review Letters, vol. 63, no. 26, pp. 2776–2779, 1989. View at Publisher · View at Google Scholar
  143. A. Albrecht and N. Turok, “Evolution of cosmic string networks,” Physical Review D, vol. 40, no. 4, pp. 973–1001, 1989. View at Publisher · View at Google Scholar
  144. D. P. Bennett and F. R. Bouchet, “High-resolution simulations of cosmic-string evolution. I. Network evolution,” Physical Review D, vol. 41, no. 8, pp. 2408–2433, 1990. View at Publisher · View at Google Scholar
  145. B. Allen and E. P. S. Shellard, “Cosmic-string evolution: a numerical simulation,” Physical Review Letters, vol. 64, no. 2, pp. 119–122, 1990. View at Google Scholar
  146. C. Ringeval, M. Sakellariadou, and F. R. Bouchet, “Cosmological evolution of cosmic string loops,” Journal of Cosmology and Astroparticle Physics, vol. 2007, no. 2, article 23, 2007. View at Publisher · View at Google Scholar
  147. C. J. A. P. Martins and E. P. S. Shellard, “Fractal properties and small-scale structure of cosmic string networks,” Physical Review D, vol. 73, no. 4, Article ID 043515, 6 pages, 2006. View at Publisher · View at Google Scholar
  148. K. D. Olum and V. Vanchurin, “Cosmic string loops in the expanding universe,” Physical Review D, vol. 75, no. 6, Article ID 063521, 2007. View at Publisher · View at Google Scholar
  149. J. Urrestilla, N. Bevis, M. Hindmarsh, M. Kunz, and A. R. Liddle, “Cosmic microwave anisotropies from BPS semilocal strings,” Journal of Cosmology and Astroparticle Physics, vol. 2008, no. 7, article 10, 2008. View at Publisher · View at Google Scholar · View at Scopus
  150. J. Urrestilla and A. Vilenkin, “Evolution of cosmic superstring networks: a numerical simulation,” Journal of High Energy Physics, vol. 2008, no. 2, article 37, 2008. View at Publisher · View at Google Scholar
  151. A. Hanany and K. Hashimoto, “Reconnection of colliding cosmic strings,” Journal of High Energy Physics, vol. 2005, no. 6, article 21, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  152. A. Achúcarro and R. De Putter, “Effective nonintercommutation of local cosmic strings at high collision speeds,” Physical Review D, vol. 74, no. 12, Article ID 121701, 2006. View at Publisher · View at Google Scholar · View at Scopus
  153. E. P. S. Shellard, “Cosmic string interactions,” Nuclear Physics B, vol. 283, pp. 624–656, 1987. View at Google Scholar
  154. R. A. Matzner, “Interaction of U(1) cosmic strings: numerical intercommutation,” Computers in Physics, vol. 2, pp. 51–64, 1988. View at Google Scholar
  155. L. M. A. Bettencourt and T. W. B. Kibble, “Non-intercommuting configurations in the collisions of type I U(1) cosmic strings,” Physics Letters B, vol. 332, no. 3-4, pp. 297–304, 1994. View at Google Scholar
  156. L. M. A. Bettencourt, P. Laguna, and R. A. Matzner, “Non-intercommuting cosmic strings,” Physical Review Letters, vol. 78, no. 11, pp. 2066–2069, 1997. View at Google Scholar
  157. P. Salmi, A. Achúcarro, E. J. Copeland, T. W. B. Kibble, R. De Putter, and D. A. Steer, “Kinematic constraints on formation of bound states of cosmic strings: field theoretical approach,” Physical Review D, vol. 77, no. 4, Article ID 041701, 2008. View at Publisher · View at Google Scholar
  158. P. Laguna and R. A. Matzner, “Numerical simulation of bosonic-superconducting-string interactions,” Physical Review D, vol. 41, no. 6, pp. 1751–1763, 1990. View at Publisher · View at Google Scholar
  159. M. G. Jackson, N. T. Jones, and J. Polchinski, “Collisions of cosmic F- and D-strings,” Journal of High Energy Physics, vol. 2005, no. 10, article 13, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  160. E. J. Copeland, T. W. B. Kibble, and D. A. Steer, “Collisions of strings with y junctions,” Physical Review Letters, vol. 97, no. 2, Article ID 021602, 2006. View at Publisher · View at Google Scholar
  161. E. J. Copeland, H. Firouzjahi, T. W. B. Kibble, and D. A. Steer, “Collision of cosmic superstrings,” Physical Review D, vol. 77, Article ID 063521, 2008. View at Publisher · View at Google Scholar
  162. N. Bevis and P. M. Saffin, “Cosmic string Y-junctions: a comparison between field theoretic and Nambu-Goto dynamics,” Physical Review D, vol. 78, no. 2, Article ID 023503, 2008. View at Publisher · View at Google Scholar
  163. P. Binetruy, A. Bohe, T. Hertog, and D .A. Steer, “Proliferation of sharp kinks on cosmic (super-)string loops with junctions,” Journal of High Energy Physics, http://arxiv.org/abs/1005.2426.
  164. T. Vachaspati and A. Vilenkin, “Formation and evolution of cosmic strings,” Physical Review D, vol. 30, no. 10, pp. 2036–2045, 1984. View at Publisher · View at Google Scholar
  165. T. W. B. Kibble, “Configuration of Z2 strings,” Physics Letters B, vol. 166, no. 3, pp. 311–313, 1986. View at Google Scholar
  166. A. Yates and T. W. B. Kibble, “An extension to models for cosmic string formation,” Physics Letters B, vol. 364, no. 3, pp. 149–156, 1995. View at Google Scholar
  167. J. Borrill, T. W. B. Kibble, T. Vachaspati, and A. Vilenkin, “Defect production in slow first-order phase transitions,” Physical Review D, vol. 52, no. 4, pp. 1934–1943, 1995. View at Publisher · View at Google Scholar
  168. R. J. Scherrer and A. Vilenkin, ““Lattice-free” simulations of topological defect formation,” Physical Review D, vol. 58, no. 10, Article ID 103501, 8 pages, 1998. View at Google Scholar
  169. R. J. Scherrer and A. Vilenkin, “Cosmic string formation from correlated fields,” Physical Review D, vol. 56, no. 2, pp. 647–652, 1997. View at Google Scholar
  170. A. Vilenkin, “Gravitational radiation from cosmic strings,” Physics Letters B, vol. 107, no. 1-2, pp. 47–50, 1981. View at Google Scholar
  171. T. Damour and A. Vilenkin, “Gravitational wave bursts from cusps and kinks on cosmic strings,” Physical Review D, vol. 64, no. 6, Article ID 064008, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  172. X. Siemens, J. Creighton, I. Maor, S. R. Majumder, K. Cannon, and J. Read, “Gravitational wave bursts from cosmic (super)strings: quantitative analysis and constraints,” Physical Review D, vol. 73, no. 10, Article ID 105001, 2006. View at Publisher · View at Google Scholar
  173. S. Olmez, V. Mandic, and X. Siemens, “Gravitational-wave stochastic background from kinks and cusps on cosmic strings,” Physical Review D, vol. 81, Article ID 104028, 10 pages, 2010. View at Publisher · View at Google Scholar
  174. T. Vachaspati, “Cosmic sparks from superconducting strings,” Physical Review Letters, vol. 101, no. 14, Article ID 141301, 2008. View at Publisher · View at Google Scholar · View at Scopus
  175. T. Vachaspati, “Cosmic rays from cosmic strings with condensates,” Physical Review D, vol. 81, no. 4, Article ID 043531, 2010. View at Google Scholar
  176. D. Austin, E. J. Copeland, and T. W. B. Kibble, “Evolution of cosmic string configurations,” Physical Review D, vol. 48, no. 12, pp. 5594–5627, 1993. View at Publisher · View at Google Scholar
  177. E. J. Copeland, T. W. B. Kibble, and D. A. Steer, “Evolution of a network of cosmic string loops,” Physical Review D, vol. 58, no. 4, Article ID 043508, 14 pages, 1998. View at Publisher · View at Google Scholar
  178. C. J. A. P. Martins and E. P .S. Shellard, “Fractal properties and small-scale structure of cosmic string networks,” Physical Review D, vol. 73, no. 4, Article ID 043515, 6 pages, 2006. View at Publisher · View at Google Scholar
  179. J. Polchinski and J. V. Rocha, “Analytic study of small scale structure on cosmic strings,” Physical Review D, vol. 74, no. 8, Article ID 083504, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  180. F. Dubath, J. Polchinski, and J. V. Rocha, “Cosmic string loops, large and small,” Physical Review D, vol. 77, no. 12, Article ID 123528, 2008. View at Publisher · View at Google Scholar
  181. E. J. Copeland and T. W. B. Kibble, “Kinks and small-scale structure on cosmic strings,” Physical Review D, vol. 80, no. 12, Article ID 123523, 7 pages, 2009. View at Publisher · View at Google Scholar
  182. J. V. Rocha, “Scaling solution for small cosmic string loops,” Physical Review Letters, vol. 100, no. 7, Article ID 071601, 2008. View at Publisher · View at Google Scholar
  183. B. Allen and E. P. S. Shellard, “Gravitational radiation from cosmic strings,” Physical Review D, vol. 45, no. 6, pp. 1898–1912, 1992. View at Publisher · View at Google Scholar
  184. X. Siemens, K. D. Olum, and A. Vilenkin, “Size of the smallest scales in cosmic string networks,” Physical Review D, vol. 66, no. 4, Article ID 043501, 4 pages, 2002. View at Publisher · View at Google Scholar
  185. G. R. Vincent, M. Hindmarsh, and M. Sakellariadou, “Scaling and small-scale structure in cosmic string networks,” Physical Review D, vol. 56, no. 2, pp. 637–646, 1997. View at Google Scholar
  186. R. Durrer and Z.-H. Zhou, “Large-scale structure formation with global topological defects,” Physical Review D, vol. 53, no. 10, pp. 5394–5410, 1996. View at Google Scholar
  187. N. Turok, “Causality and the Doppler peaks,” Physical Review D, vol. 54, no. 6, pp. R3686–R3689, 1996. View at Publisher · View at Google Scholar
  188. U.-L. Pen, U. Seljak, and N. Turok, “Power spectra in global defect theories of cosmic structure formation,” Physical Review Letters, vol. 79, no. 9, pp. 1611–1614, 1997. View at Google Scholar
  189. R. Durrer and M. Kunz, “Cosmic microwave background anisotropies from scaling seeds: generic properties of the correlation functions,” Physical Review D, vol. 57, no. 6, pp. R3199–R3203, 1998. View at Publisher · View at Google Scholar
  190. C. Contaldi, M. Hindmarsh, and J. Magueijo, “Power spectra of the cosmic microwave background and density fluctuations seeded by local cosmic strings,” Physical Review Letters, vol. 82, no. 4, pp. 679–682, 1999. View at Google Scholar
  191. J.-H. P. Wu, P. P. Avelino, E. P. S. Shellard, and B. Allen, “Cosmic strings, loops, and linear growth of matter perturbations,” International Journal of Modern Physics D, vol. 11, no. 1, pp. 61–102, 2002. View at Publisher · View at Google Scholar
  192. N. Bevis, M. Hindmarsh, M. Kunz, and J. Urrestilla, “CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model,” Physical Review D, vol. 75, no. 6, Article ID 065015, 2007. View at Publisher · View at Google Scholar
  193. N. Bevis, M. Hindmarsh, M. Kunz, and J. Urrestilla, “CMB power spectra from cosmic strings: predictions for the Planck satellite and beyond,” Journal of High Energy Physics, http://arxiv.org/abs/1005.2663.
  194. N. Bevis, M. Hindmarsh, M. Kunz, and J. Urrestilla, “CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model,” Physical Review D, vol. 75, no. 6, Article ID 065015, 22 pages, 2007. View at Publisher · View at Google Scholar
  195. J. Magueijo, A. Albrecht, D. Coulson, and P. Ferreira, “Doppler peaks from active perturbations,” Physical Review Letters, vol. 76, no. 15, pp. 2617–2620, 1996. View at Google Scholar
  196. N. Bevis, M. Hindmarsh, M. Kunz, and J. Urrestilla, “Fitting cosmic microwave background data with cosmic strings and inflation,” Physical Review Letters, vol. 100, no. 2, Article ID 021301, 4 pages, 2008. View at Publisher · View at Google Scholar
  197. D. P. Bennett, A. Stebbins, and F. R. Bouchet, “The implications of the COBE diffuse microwave radiation results for cosmic strings,” Astrophysical Journal, vol. 399, no. 1, pp. L5–L8, 1992. View at Google Scholar
  198. U.-L. Pen, D. N. Spergel, and N. Turok, “Cosmic structure formation and microwave anisotropies from global field ordering,” Physical Review D, vol. 49, no. 2, pp. 692–729, 1994. View at Publisher · View at Google Scholar
  199. B. Allen, R. R. Caldwell, S. Dodelson, L. Knox, E. P. S. Shellard, and A. Stebbins, “Cosmic microwave background anisotropy induced by cosmic strings on angular scales 15,” Physical Review Letters, vol. 79, no. 14, pp. 2624–2627, 1997. View at Google Scholar
  200. M. Landriau and E. P. S. Shellard, “Fluctuations in the cosmic microwave background induced by cosmic strings: methods and formalism,” Physical Review D, vol. 67, no. 10, Article ID 103512, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  201. M. Landriau and E. P.S. Shellard, “Large angle cosmic microwave background fluctuations from cosmic strings with a cosmological constant,” Physical Review D, vol. 69, no. 2, Article ID 023003, 2004. View at Publisher · View at Google Scholar
  202. A. A. Fraisse, C. Ringeval, D. N. Spergel, and F. R. Bouchet, “Small-angle CMB temperature anisotropies induced by cosmic strings,” Physical Review D, vol. 78, no. 4, Article ID 043535, 2008. View at Publisher · View at Google Scholar
  203. M. Hindmarsh, “Small-scale microwave background fluctuations from cosmic strings,” Astrophysical Journal, vol. 431, no. 2, pp. 534–542, 1994. View at Google Scholar
  204. A. Stebbins and S. Veeraraghavan, “Beyond the small-angle approximation for MBR anisotropy from seeds,” Physical Review D, vol. 51, no. 4, pp. 1465–1478, 1995. View at Publisher · View at Google Scholar
  205. J. R. Gott III, C. Park, R. Juszkiewicz, W. E. Bies, D. P. Bennett, F. R. Bouchet, and A. Stebbins, “Topology of microwave background fluctuations: theory,” Astrophysical Journal, vol. 352, no. 1, pp. 1–14, 1990. View at Google Scholar
  206. K. Takahashi, A. Naruko, Y. Sendouda, D. Yamauchi, C.-M. Yoo, and M. Sasaki, “Non-Gaussianity in the cosmic microwave background temperature fluctuations from cosmic (super-)strings,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 10, article 3, 2009. View at Publisher · View at Google Scholar
  207. K. Falconer, Fractal Geometry, John Wiley & Sons, Chichester, UK, 2006.
  208. M. P. Pompilio, F. R. Bouchet, G. Murante, and A. Provenzale, “Multifractal analysis of string-induced cosmic microwave background radiation anisotropies,” Astrophysical Journal, vol. 449, no. 1, pp. 1–8, 1995. View at Google Scholar
  209. M. P. Hobson, A. W. Jones, and A. N. Lasenby, “Wavelet analysis and the detection of non-Gaussianity in the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 309, no. 1, pp. 125–140, 1999. View at Google Scholar
  210. R. B. Barreiro and M. P. Hobson, “The discriminating power of wavelets to detect non-Gaussianity in the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 327, no. 3, pp. 813–828, 2001. View at Publisher · View at Google Scholar
  211. D. K. Hammond, Y. Wiaux, and P. Vandergheynst, “Wavelet domain Bayesian denoising of string signal in the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 398, no. 3, pp. 1317–1332, 2009. View at Publisher · View at Google Scholar
  212. M. Hindmarsh, C. Ringeval, and T. Suyama, “CMB temperature bispectrum induced by cosmic strings,” Physical Review D, vol. 80, no. 8, Article ID 083501, 2009. View at Publisher · View at Google Scholar
  213. D. N. Spergel and D. M. Goldberg, “Microwave background bispectrum. I. Basic formalism,” Physical Review D, vol. 59, no. 10, Article ID 103001, 8 pages, 1999. View at Publisher · View at Google Scholar
  214. N. Aghanim, M. Kunz, P. G. Castro, and O. Forni, “Non-gaussianity: comparing wavelet and Fourier based methods,” Astronomy and Astrophysics, vol. 406, no. 3, pp. 797–816, 2003. View at Google Scholar
  215. M. Hindmarsh, C. Ringeval, and T. Suyama, “CMB temperature trispectrum of cosmic strings,” Physical Review D, vol. 81, no. 6, Article ID 063505, 2010. View at Publisher · View at Google Scholar
  216. N. Bartolo, E. Komatsu, S. Matarrese, and A. Riotto, “Non-Gaussianity from inflation: theory and observations,” Physics Reports, vol. 402, no. 3-4, pp. 103–266, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  217. K. M. Smith, L. Senatore, and M. Zaldarriaga, “Optimal limits on fNLlocal from WMAP 5-year data,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 9, 2009. View at Publisher · View at Google Scholar
  218. D. M. Regan and E. P. S. Shellard, “General CMB and primordial trispectrum estimatio,” Journal of Cosmology and Astroparticle Physics, http://arxiv.org/abs/1004.2915.
  219. M. Sakellariadou, “A note on the evolution of cosmic string/superstring networks,” Journal of Cosmology and Astroparticle Physics, no. 4, article 3, pp. 103–116, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  220. A. Avgoustidis and E. P. S. Shellard, “Velocity-dependent models for non-Abelian/entangled string networks,” Physical Review D, vol. 78, no. 10, Article ID 103510, 21 pages, 2008. View at Publisher · View at Google Scholar
  221. D. M. Regan and E. P. S. Shellard, “Cosmic string power spectrum, bispectrum and trispectrum,” Journal of Cosmology and Astroparticle Physics, http://arxiv.org/abs/0911.2491.
  222. M. Landriau and E. P. S. Shellard, “Cosmic string induced CMB maps,” Journal of Cosmology and Astroparticle Physics, http://arxiv.org/abs/1004.2885.