Parity Violating Statistical Anisotropy



Particle production of an Abelian vector boson field with an axial coupling is investigated. The conditions for the generation of scale invariant spectra for the vector field transverse components are obtained. If the vector field contributes to the curvature perturbation in the Universe, scale-invariant particle production enables it to give rise to statistical anisotropy in the spectrum and bispectrum of cosmological perturbations. The axial coupling allows particle production to be parity violating, which in turn can generate parity violating signatures in the bispectrum. The conditions for parity violation are derived and the observational signatures are obtained in the context of the vectorcurvaton paradigm. Two concrete examples are presented based on realistic particle theory.


Cosmology of Theories beyond the SM String Field Theory 


  1. [1]
    K. Dimopoulos, Can a vector field be responsible for the curvature perturbation in the Universe?, Phys. Rev. D 74 (2006) 083502 [hep-ph/0607229] [INSPIRE].MathSciNetADSGoogle Scholar
  2. [2]
    K. Dimopoulos, Statistical anisotropy and the vector curvaton paradigm, Int. J. Mod. Phys. D 21 (2012) 1250023 [arXiv:1107.2779] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    S. Mollerach, Isocurvature baryon perturbations and inflation, Phys. Rev. D 42 (1990) 313 [INSPIRE].ADSGoogle Scholar
  4. [4]
    A.D. Linde and V.F. Mukhanov, Non-gaussian isocurvature perturbations from inflation, Phys. Rev. D 56 (1997) 535 [astro-ph/9610219] [INSPIRE].ADSGoogle Scholar
  5. [5]
    D.H. Lyth and D. Wands, Generating the curvature perturbation without an inflaton, Phys. Lett. B 524 (2002) 5 [hep-ph/0110002] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    K. Enqvist and M.S. Sloth, Adiabatic CMB perturbations in pre-big bang string cosmology, Nucl. Phys. B 626 (2002) 395 [hep-ph/0109214] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    T. Moroi and T. Takahashi, Effects of cosmological moduli fields on cosmic microwave background, Phys. Lett. B 522 (2001) 215 [Erratum ibid. B 539 (2002) 303] [hep-ph/0110096] [INSPIRE].
  8. [8]
    S. Yokoyama and J. Soda, Primordial statistical anisotropy generated at the end of inflation, JCAP 08 (2008) 005 [arXiv:0805.4265] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    M. Shiraishi and S. Yokoyama, Violation of the rotational invariance in the CMB bispectrum, Prog. Theor. Phys. 126 (2011) 923 [arXiv:1107.0682] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  10. [10]
    K. Dimopoulos, M. Karciauskas, D.H. Lyth and Y. Rodriguez, Statistical anisotropy of the curvature perturbation from vector field perturbations, JCAP 05 (2009) 013 [arXiv:0809.1055] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Karciauskas, K. Dimopoulos and D.H. Lyth, Anisotropic non-gaussianity from vector field perturbations, Phys. Rev. D 80 (2009) 023509 [Erratum ibid. D 85 (2012) 069905] [arXiv:0812.0264] [INSPIRE].Google Scholar
  12. [12]
    E. Dimastrogiovanni, N. Bartolo, S. Matarrese and A. Riotto, Non-gaussianity and statistical anisotropy from vector field populated inflationary models, Adv. Astron. 2010 (2010) 752670 [arXiv:1001.4049] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    C.A. Valenzuela-Toledo, Y. Rodriguez and D.H. Lyth, Non-gaussianity at tree- and one-loop levels from vector field perturbations, Phys. Rev. D 80 (2009) 103519 [arXiv:0909.4064] [INSPIRE].ADSGoogle Scholar
  14. [14]
    C.A. Valenzuela-Toledo and Y. Rodriguez, Non-gaussianity from the trispectrum and vector field perturbations, Phys. Lett. B 685 (2010) 120 [arXiv:0910.4208] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    C.A. Valenzuela-Toledo, Y. Rodriguez and J.P. Beltran Almeida, Feynman-like rules for calculating n-point correlators of the primordial curvature perturbation, JCAP 10 (2011) 020 [arXiv:1107.3186] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    A.R. Pullen and M. Kamionkowski, Cosmic microwave background statistics for a direction-dependent primordial power spectrum, Phys. Rev. D 76 (2007) 103529 [arXiv:0709.1144] [INSPIRE].ADSGoogle Scholar
  17. [17]
    N.E. Groeneboom and H.K. Eriksen, Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data, Astrophys. J. 690 (2009) 1807 [arXiv:0807.2242] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    N.E. Groeneboom, L. Ackerman, I.K. Wehus and H.K. Eriksen, Bayesian analysis of an anisotropic universe model: systematics and polarization, Astrophys. J. 722 (2010) 452 [arXiv:0911.0150] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    D. Hanson and A. Lewis, Estimators for CMB statistical anisotropy, Phys. Rev. D 80 (2009) 063004 [arXiv:0908.0963] [INSPIRE].ADSGoogle Scholar
  20. [20]
    Y.-Z. Ma, G. Efstathiou and A. Challinor, Testing a direction-dependent primordial power spectrum with observations of the cosmic microwave background, Phys. Rev. D 83 (2011) 083005 [arXiv:1102.4961] [INSPIRE].ADSGoogle Scholar
  21. [21]
    O. Rudjord et al., Directional variations of the non-gaussianity parameter f N L, Astrophys. J. 708 (2010) 1321 [arXiv:0906.3232] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    N. Bartolo, E. Dimastrogiovanni, M. Liguori, S. Matarrese and A. Riotto, An estimator for statistical anisotropy from the CMB bispectrum, JCAP 01 (2012) 029 [arXiv:1107.4304] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    C. Pitrou, T.S. Pereira and J.-P. Uzan, Predictions from an anisotropic inflationary era, JCAP 04 (2008) 004 [arXiv:0801.3596] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    S. Kanno, M. Kimura, J. Soda and S. Yokoyama, Anisotropic inflation from vector impurity, JCAP 08 (2008) 034 [arXiv:0806.2422] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    M.-a. Watanabe, S. Kanno and J. Soda, Imprints of anisotropic inflation on the cosmic microwave background, Mon. Not. Roy. Astron. Soc. 412 (2011) L83 [arXiv:1011.3604] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M.-a. Watanabe, S. Kanno and J. Soda, The nature of primordial fluctuations from anisotropic inflation, Prog. Theor. Phys. 123 (2010) 1041 [arXiv:1003.0056] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  27. [27]
    T.R. Dulaney and M.I. Gresham, Primordial power spectra from anisotropic inflation, Phys. Rev. D 81 (2010) 103532 [arXiv:1001.2301] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Gumrukcuoglu, B. Himmetoglu and M. Peloso, Scalar-scalar, scalar-tensor and tensor-tensor correlators from anisotropic inflation, Phys. Rev. D 81 (2010) 063528 [arXiv:1001.4088] [INSPIRE].ADSGoogle Scholar
  29. [29]
    B. Himmetoglu, Spectrum of perturbations in anisotropic inflationary universe with vector hair, JCAP 03 (2010) 023 [arXiv:0910.3235] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S. Kanno, J. Soda and M.-a. Watanabe, Anisotropic power-law inflation, JCAP 12 (2010) 024 [arXiv:1010.5307] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    J.M. Wagstaff and K. Dimopoulos, Particle production of vector fields: scale invariance is attractive, Phys. Rev. D 83 (2011) 023523 [arXiv:1011.2517] [INSPIRE].ADSGoogle Scholar
  32. [32]
    J. Soda, Statistical anisotropy from anisotropic inflation, Class. Quant. Grav. 29 (2012) 083001 [arXiv:1201.6434] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    M.-a. Watanabe, S. Kanno and J. Soda, Inflationary universe with anisotropic hair, Phys. Rev. Lett. 102 (2009) 191302 [arXiv:0902.2833] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S. Hervik, D.F. Mota and M. Thorsrud, Inflation with stable anisotropic hair: is it cosmologically viable?, JHEP 11 (2011) 146 [arXiv:1109.3456] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    N. Barnaby and M. Peloso, Large nongaussianity in axion inflation, Phys. Rev. Lett. 106 (2011) 181301 [arXiv:1011.1500] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    N. Barnaby, R. Namba and M. Peloso, Phenomenology of a pseudo-scalar inflaton: naturally large nongaussianity, JCAP 04 (2011) 009 [arXiv:1102.4333] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    K. Dimopoulos, Supergravity inspired vector curvaton, Phys. Rev. D 76 (2007) 063506 [arXiv:0705.3334] [INSPIRE].MathSciNetADSGoogle Scholar
  38. [38]
    K. Dimopoulos and M. Karciauskas, Non-minimally coupled vector curvaton, JHEP 07 (2008) 119 [arXiv:0803.3041] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    K. Dimopoulos, M. Karciauskas and J.M. Wagstaff, Vector curvaton with varying kinetic function, Phys. Rev. D 81 (2010) 023522 [arXiv:0907.1838] [INSPIRE].ADSGoogle Scholar
  40. [40]
    K. Dimopoulos, M. Karciauskas and J.M. Wagstaff, Vector curvaton without instabilities, Phys. Lett. B 683 (2010) 298 [arXiv:0909.0475] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    K. Dimopoulos, D. Wills and I. Zavala, Statistical anisotropy from vector curvaton in D-brane inflation, arXiv:1108.4424 [INSPIRE].
  42. [42]
    K. Dimopoulos, G. Lazarides and J.M. Wagstaff, Eliminating the η-problem in SUGRA hybrid inflation with vector backreaction, JCAP 02 (2012) 018 [arXiv:1111.1929] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    A. Golovnev, V. Mukhanov and V. Vanchurin, Vector inflation, JCAP 06 (2008) 009 [arXiv:0802.2068] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    A. Golovnev, V. Mukhanov and V. Vanchurin, Gravitational waves in vector inflation, JCAP 11 (2008) 018 [arXiv:0810.4304] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    T. Chiba, Initial conditions for vector inflation, JCAP 08 (2008) 004 [arXiv:0805.4660] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    A. Golovnev and V. Vanchurin, Cosmological perturbations from vector inflation, Phys. Rev. D 79 (2009) 103524 [arXiv:0903.2977] [INSPIRE].ADSGoogle Scholar
  47. [47]
    A. Golovnev, Linear perturbations in vector inflation and stability issues, Phys. Rev. D 81 (2010) 023514 [arXiv:0910.0173] [INSPIRE].ADSGoogle Scholar
  48. [48]
    Y. Zhang, The slow-roll and rapid-roll conditions in the space-like vector field scenario, Phys. Rev. D 80 (2009) 043519 [arXiv:0903.3269] [INSPIRE].ADSGoogle Scholar
  49. [49]
    M.S. Turner and L.M. Widrow, Inflation produced, large scale magnetic fields, Phys. Rev. D 37 (1988) 2743 [INSPIRE].ADSGoogle Scholar
  50. [50]
    B. Himmetoglu, C.R. Contaldi and M. Peloso, Instability of the ACW model and problems with massive vectors during inflation, Phys. Rev. D 79 (2009) 063517 [arXiv:0812.1231] [INSPIRE].ADSGoogle Scholar
  51. [51]
    B. Himmetoglu, C.R. Contaldi and M. Peloso, Instability of anisotropic cosmological solutions supported by vector fields, Phys. Rev. Lett. 102 (2009) 111301 [arXiv:0809.2779] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    B. Himmetoglu, C.R. Contaldi and M. Peloso, Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature, Phys. Rev. D 80 (2009) 123530 [arXiv:0909.3524] [INSPIRE].ADSGoogle Scholar
  53. [53]
    M. Karciauskas and D.H. Lyth, On the health of a vector field with (RA 2)/6 coupling to gravity, JCAP 11 (2010) 023 [arXiv:1007.1426] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    M. Giovannini, On the variation of the gauge couplings during inflation, Phys. Rev. D 64 (2001) 061301 [astro-ph/0104290] [INSPIRE].ADSGoogle Scholar
  55. [55]
    K. Bamba and J. Yokoyama, Large scale magnetic fields from inflation in dilaton electromagnetism, Phys. Rev. D 69 (2004) 043507 [astro-ph/0310824] [INSPIRE].ADSGoogle Scholar
  56. [56]
    K. Bamba and J. Yokoyama, Large-scale magnetic fields from dilaton inflation in noncommutative spacetime, Phys. Rev. D 70 (2004) 083508 [hep-ph/0409237] [INSPIRE].ADSGoogle Scholar
  57. [57]
    O. Bertolami and R. Monteiro, Varying electromagnetic coupling and primordial magnetic fields, Phys. Rev. D 71 (2005) 123525 [astro-ph/0504211] [INSPIRE].ADSGoogle Scholar
  58. [58]
    J. Salim, N. Souza, S.E. Perez Bergliaffa and T. Prokopec, Creation of cosmological magnetic fields in a bouncing cosmology, JCAP 04 (2007) 011 [astro-ph/0612281] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    K. Bamba and M. Sasaki, Large-scale magnetic fields in the inflationary universe, JCAP 02 (2007) 030 [astro-ph/0611701] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    J. Martin and J. Yokoyama, Generation of large-scale magnetic fields in single-field inflation, JCAP 01 (2008) 025 [arXiv:0711.4307] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    K. Bamba and S.D. Odintsov, Inflation and late-time cosmic acceleration in non-minimal Maxwell-F (R) gravity and the generation of large-scale magnetic fields, JCAP 04 (2008) 024 [arXiv:0801.0954] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    K. Bamba, C. Geng and S. Ho, Large-scale magnetic fields from inflation due to Chern-Simons-like effective interaction, JCAP 11 (2008) 013 [arXiv:0806.1856] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    V. Demozzi, V. Mukhanov and H. Rubinstein, Magnetic fields from inflation?, JCAP 08 (2009) 025 [arXiv:0907.1030] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    R. Emami, H. Firouzjahi and M.S. Movahed, Inflation from charged scalar and primordial magnetic fields?, Phys. Rev. D 81 (2010) 083526 [arXiv:0908.4161] [INSPIRE].ADSGoogle Scholar
  65. [65]
    S. Kanno, J. Soda and M.-a. Watanabe, Cosmological magnetic fields from inflation and backreaction, JCAP 12 (2009) 009 [arXiv:0908.3509] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    C. Bonvin, C. Caprini and R. Durrer, Magnetic fields from inflation: the transition to the radiation era, arXiv:1112.3901 [INSPIRE].
  67. [67]
    N. Barnaby, R. Namba and M. Peloso, Observable non-gaussianity from gauge field production in slow roll inflation and a challenging connection with magnetogenesis, arXiv:1202.1469 [INSPIRE].
  68. [68]
    M. Karčiauskas, The primordial curvature perturbation from vector fields of general non-abelian groups, JCAP 01 (2012) 014 [arXiv:1104.3629] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    W.D. Garretson, G.B. Field and S.M. Carroll, Primordial magnetic fields from pseudoGoldstone bosons, Phys. Rev. D 46 (1992) 5346 [hep-ph/9209238] [INSPIRE].ADSGoogle Scholar
  70. [70]
    J.M. Cornwall, Speculations on primordial magnetic helicity, Phys. Rev. D 56 (1997) 6146 [hep-th/9704022] [INSPIRE].ADSGoogle Scholar
  71. [71]
    R. Brustein and D.H. Oaknin, Amplification of hypercharge electromagnetic fields by a cosmological pseudoscalar, Phys. Rev. D 60 (1999) 023508 [hep-ph/9901242] [INSPIRE].ADSGoogle Scholar
  72. [72]
    G.B. Field and S.M. Carroll, Cosmological magnetic fields from primordial helicity, Phys. Rev. D 62 (2000) 103008 [astro-ph/9811206] [INSPIRE].ADSGoogle Scholar
  73. [73]
    F. Finelli and A. Gruppuso, Resonant amplification of gauge fields in expanding universe, Phys. Lett. B 502 (2001) 216 [hep-ph/0001231] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    L. Campanelli and M. Giannotti, Magnetic helicity generation from the cosmic axion field, Phys. Rev. D 72 (2005) 123001 [astro-ph/0508653] [INSPIRE].ADSGoogle Scholar
  75. [75]
    L. Campanelli and M. Giannotti, Production of axions by cosmic magnetic helicity, Phys. Rev. Lett. 96 (2006) 161302 [astro-ph/0512458] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    M.M. Anber and L. Sorbo, N-flationary magnetic fields, JCAP 10 (2006) 018 [astro-ph/0606534] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    A.A. Andrianov, F. Cannata, A.Y. Kamenshchik and D. Regoli, Two-field cosmological models and large-scale cosmic magnetic fields, JCAP 10 (2008) 019 [arXiv:0806.1844] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    L. Campanelli, Helical magnetic fields from inflation, Int. J. Mod. Phys. D 18 (2009) 1395 [arXiv:0805.0575] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    R. Durrer, L. Hollenstein and R.K. Jain, Can slow roll inflation induce relevant helical magnetic fields?, JCAP 03 (2011) 037 [arXiv:1005.5322] [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    M.M. Anber and L. Sorbo, Naturally inflating on steep potentials through electromagnetic dissipation, Phys. Rev. D 81 (2010) 043534 [arXiv:0908.4089] [INSPIRE].ADSGoogle Scholar
  81. [81]
    K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    F.C. Adams, J.R. Bond, K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation: particle physics models, power law spectra for large scale structure and constraints from COBE, Phys. Rev. D 47 (1993) 426 [hep-ph/9207245] [INSPIRE].ADSGoogle Scholar
  83. [83]
    L. Knox and A. Olinto, Initial conditions for natural inflation, Phys. Rev. D 48 (1993) 946 [INSPIRE].ADSGoogle Scholar
  84. [84]
    K. Freese and W.H. Kinney, On: natural inflation, Phys. Rev. D 70 (2004) 083512 [hep-ph/0404012] [INSPIRE].ADSGoogle Scholar
  85. [85]
    L. Sorbo, Parity violation in the cosmic microwave background from a pseudoscalar inflaton, JCAP 06 (2011) 003 [arXiv:1101.1525] [INSPIRE].ADSCrossRefGoogle Scholar
  86. [86]
    J.L. Cook and L. Sorbo, Particle production during inflation and gravitational waves detectable by ground-based interferometers, Phys. Rev. D 85 (2012) 023534 [arXiv:1109.0022] [INSPIRE].ADSGoogle Scholar
  87. [87]
    N. Barnaby, E. Pajer and M. Peloso, Gauge field production in axion inflation: consequences for monodromy, non-gaussianity in the CMB and gravitational waves at interferometers, Phys. Rev. D 85 (2012) 023525 [arXiv:1110.3327] [INSPIRE].ADSGoogle Scholar
  88. [88]
    J.M. Maldacena and G.L. Pimentel, On graviton non-gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    J. Soda, H. Kodama and M. Nozawa, Parity violation in graviton non-gaussianity, JHEP 08 (2011) 067 [arXiv:1106.3228] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    M. Shiraishi, D. Nitta and S. Yokoyama, Parity violation of gravitons in the CMB bispectrum, Prog. Theor. Phys. 126 (2011) 937 [arXiv:1108.0175] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  91. [91]
    E. Komatsu et al., Non-gaussianity as a probe of the physics of the primordial universe and the astrophysics of the low redshift universe, arXiv:0902.4759 [INSPIRE].
  92. [92]
    N. Bartolo, E. Dimastrogiovanni, S. Matarrese and A. Riotto, Anisotropic bispectrum of curvature perturbations from primordial non-abelian vector fields, JCAP 10 (2009) 015 [arXiv:0906.4944] [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    N. Bartolo, E. Dimastrogiovanni, S. Matarrese and A. Riotto, Anisotropic trispectrum of curvature perturbations induced by primordial non-abelian vector fields, JCAP 11 (2009) 028 [arXiv:0909.5621] [INSPIRE].ADSCrossRefGoogle Scholar
  94. [94]
    K. Murata and J. Soda, Anisotropic inflation with non-abelian gauge kinetic function, JCAP 06 (2011) 037 [arXiv:1103.6164] [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    A. Maleknejad and M. Sheikh-Jabbari, Gauge-flation: inflation from non-abelian gauge fields, arXiv:1102.1513 [INSPIRE].
  96. [96]
    A. Maleknejad, M. Sheikh-Jabbari and J. Soda, Gauge-flation and cosmic no-hair conjecture, JCAP 01 (2012) 016 [arXiv:1109.5573] [INSPIRE].ADSCrossRefGoogle Scholar
  97. [97]
    L. Ackerman, S.M. Carroll and M.B. Wise, Imprints of a Primordial Preferred Direction on the Microwave Background, Phys. Rev. D 75 (2007) 083502 [Erratum ibid. D 80 (2009) 069901] [astro-ph/0701357] [INSPIRE].
  98. [98]
    E. Akofor, A. Balachandran, S. Jo, A. Joseph and B. Qureshi, Direction-dependent CMB power spectrum and statistical anisotropy from noncommutative geometry, JHEP 05 (2008) 092 [arXiv:0710.5897] [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    A.R. Liddle and D.H. Lyth, The primordial density perturbation: cosmology, inflation and the origin of structure, Cambridge University Press, Cambridge U.K. (2009).Google Scholar
  100. [100]
    B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, New cosmological constraints on primordial black holes, Phys. Rev. D 81 (2010) 104019 [arXiv:0912.5297] [INSPIRE].ADSGoogle Scholar
  101. [101]
    D.H. Lyth, Primordial black hole formation and hybrid inflation, arXiv:1107.1681 [INSPIRE].
  102. [102]
    E.J. Chun, K. Dimopoulos and D. Lyth, Curvaton and QCD axion in supersymmetric theories, Phys. Rev. D 70 (2004) 103510 [hep-ph/0402059] [INSPIRE].ADSGoogle Scholar
  103. [103]
    K. Dimopoulos, Inflation at the TeV scale with a PNGB curvaton, Phys. Lett. B 634 (2006) 331 [hep-th/0511268] [INSPIRE].ADSCrossRefGoogle Scholar
  104. [104]
    K. Dimopoulos and G. Lazarides, Modular inflation and the orthogonal axion as curvaton, Phys. Rev. D 73 (2006) 023525 [hep-ph/0511310] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Konstantinos Dimopoulos
    • 1
  • Mindaugas Karčiauskas
    • 2
  1. 1.Consortium for Fundamental Physics, Physics DepartmentLancaster UniversityLancasterUK
  2. 2.CAFPE and Departamento de Física Teórica y del CosmosUniversidad de GranadaGranadaSpain

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