Skip to main content
SpringerLink
Log in

Parity Violating Statistical Anisotropy

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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].

    MathSciNet  ADS  Google Scholar 

  2. K. Dimopoulos, Statistical anisotropy and the vector curvaton paradigm, Int. J. Mod. Phys. D 21 (2012) 1250023 [arXiv:1107.2779] [INSPIRE].

    Article  ADS  Google Scholar 

  3. S. Mollerach, Isocurvature baryon perturbations and inflation, Phys. Rev. D 42 (1990) 313 [INSPIRE].

    ADS  Google Scholar 

  4. A.D. Linde and V.F. Mukhanov, Non-gaussian isocurvature perturbations from inflation, Phys. Rev. D 56 (1997) 535 [astro-ph/9610219] [INSPIRE].

    ADS  Google Scholar 

  5. D.H. Lyth and D. Wands, Generating the curvature perturbation without an inflaton, Phys. Lett. B 524 (2002) 5 [hep-ph/0110002] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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. S. Yokoyama and J. Soda, Primordial statistical anisotropy generated at the end of inflation, JCAP 08 (2008) 005 [arXiv:0805.4265] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  MATH  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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. 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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  19. D. Hanson and A. Lewis, Estimators for CMB statistical anisotropy, Phys. Rev. D 80 (2009) 063004 [arXiv:0908.0963] [INSPIRE].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  21. O. Rudjord et al., Directional variations of the non-gaussianity parameter f N L , Astrophys. J. 708 (2010) 1321 [arXiv:0906.3232] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  23. C. Pitrou, T.S. Pereira and J.-P. Uzan, Predictions from an anisotropic inflationary era, JCAP 04 (2008) 004 [arXiv:0801.3596] [INSPIRE].

    Article  ADS  Google Scholar 

  24. S. Kanno, M. Kimura, J. Soda and S. Yokoyama, Anisotropic inflation from vector impurity, JCAP 08 (2008) 034 [arXiv:0806.2422] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  MATH  Google Scholar 

  27. T.R. Dulaney and M.I. Gresham, Primordial power spectra from anisotropic inflation, Phys. Rev. D 81 (2010) 103532 [arXiv:1001.2301] [INSPIRE].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  29. B. Himmetoglu, Spectrum of perturbations in anisotropic inflationary universe with vector hair, JCAP 03 (2010) 023 [arXiv:0910.3235] [INSPIRE].

    Article  ADS  Google Scholar 

  30. S. Kanno, J. Soda and M.-a. Watanabe, Anisotropic power-law inflation, JCAP 12 (2010) 024 [arXiv:1010.5307] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  32. J. Soda, Statistical anisotropy from anisotropic inflation, Class. Quant. Grav. 29 (2012) 083001 [arXiv:1201.6434] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. M.-a. Watanabe, S. Kanno and J. Soda, Inflationary universe with anisotropic hair, Phys. Rev. Lett. 102 (2009) 191302 [arXiv:0902.2833] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  35. N. Barnaby and M. Peloso, Large nongaussianity in axion inflation, Phys. Rev. Lett. 106 (2011) 181301 [arXiv:1011.1500] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  37. K. Dimopoulos, Supergravity inspired vector curvaton, Phys. Rev. D 76 (2007) 063506 [arXiv:0705.3334] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  38. K. Dimopoulos and M. Karciauskas, Non-minimally coupled vector curvaton, JHEP 07 (2008) 119 [arXiv:0803.3041] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  40. K. Dimopoulos, M. Karciauskas and J.M. Wagstaff, Vector curvaton without instabilities, Phys. Lett. B 683 (2010) 298 [arXiv:0909.0475] [INSPIRE].

    Article  ADS  Google Scholar 

  41. K. Dimopoulos, D. Wills and I. Zavala, Statistical anisotropy from vector curvaton in D-brane inflation, arXiv:1108.4424 [INSPIRE].

  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].

    Article  ADS  Google Scholar 

  43. A. Golovnev, V. Mukhanov and V. Vanchurin, Vector inflation, JCAP 06 (2008) 009 [arXiv:0802.2068] [INSPIRE].

    Article  ADS  Google Scholar 

  44. A. Golovnev, V. Mukhanov and V. Vanchurin, Gravitational waves in vector inflation, JCAP 11 (2008) 018 [arXiv:0810.4304] [INSPIRE].

    Article  ADS  Google Scholar 

  45. T. Chiba, Initial conditions for vector inflation, JCAP 08 (2008) 004 [arXiv:0805.4660] [INSPIRE].

    Article  ADS  Google Scholar 

  46. A. Golovnev and V. Vanchurin, Cosmological perturbations from vector inflation, Phys. Rev. D 79 (2009) 103524 [arXiv:0903.2977] [INSPIRE].

    ADS  Google Scholar 

  47. A. Golovnev, Linear perturbations in vector inflation and stability issues, Phys. Rev. D 81 (2010) 023514 [arXiv:0910.0173] [INSPIRE].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  49. M.S. Turner and L.M. Widrow, Inflation produced, large scale magnetic fields, Phys. Rev. D 37 (1988) 2743 [INSPIRE].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  54. M. Giovannini, On the variation of the gauge couplings during inflation, Phys. Rev. D 64 (2001) 061301 [astro-ph/0104290] [INSPIRE].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  57. O. Bertolami and R. Monteiro, Varying electromagnetic coupling and primordial magnetic fields, Phys. Rev. D 71 (2005) 123525 [astro-ph/0504211] [INSPIRE].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  59. K. Bamba and M. Sasaki, Large-scale magnetic fields in the inflationary universe, JCAP 02 (2007) 030 [astro-ph/0611701] [INSPIRE].

    Article  ADS  Google Scholar 

  60. J. Martin and J. Yokoyama, Generation of large-scale magnetic fields in single-field inflation, JCAP 01 (2008) 025 [arXiv:0711.4307] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  63. V. Demozzi, V. Mukhanov and H. Rubinstein, Magnetic fields from inflation?, JCAP 08 (2009) 025 [arXiv:0907.1030] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  65. S. Kanno, J. Soda and M.-a. Watanabe, Cosmological magnetic fields from inflation and backreaction, JCAP 12 (2009) 009 [arXiv:0908.3509] [INSPIRE].

    Article  ADS  Google Scholar 

  66. C. Bonvin, C. Caprini and R. Durrer, Magnetic fields from inflation: the transition to the radiation era, arXiv:1112.3901 [INSPIRE].

  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. M. Karčiauskas, The primordial curvature perturbation from vector fields of general non-abelian groups, JCAP 01 (2012) 014 [arXiv:1104.3629] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  70. J.M. Cornwall, Speculations on primordial magnetic helicity, Phys. Rev. D 56 (1997) 6146 [hep-th/9704022] [INSPIRE].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  72. G.B. Field and S.M. Carroll, Cosmological magnetic fields from primordial helicity, Phys. Rev. D 62 (2000) 103008 [astro-ph/9811206] [INSPIRE].

    ADS  Google Scholar 

  73. F. Finelli and A. Gruppuso, Resonant amplification of gauge fields in expanding universe, Phys. Lett. B 502 (2001) 216 [hep-ph/0001231] [INSPIRE].

    Article  ADS  Google Scholar 

  74. L. Campanelli and M. Giannotti, Magnetic helicity generation from the cosmic axion field, Phys. Rev. D 72 (2005) 123001 [astro-ph/0508653] [INSPIRE].

    ADS  Google Scholar 

  75. L. Campanelli and M. Giannotti, Production of axions by cosmic magnetic helicity, Phys. Rev. Lett. 96 (2006) 161302 [astro-ph/0512458] [INSPIRE].

    Article  ADS  Google Scholar 

  76. M.M. Anber and L. Sorbo, N-flationary magnetic fields, JCAP 10 (2006) 018 [astro-ph/0606534] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  78. L. Campanelli, Helical magnetic fields from inflation, Int. J. Mod. Phys. D 18 (2009) 1395 [arXiv:0805.0575] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  81. K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  83. L. Knox and A. Olinto, Initial conditions for natural inflation, Phys. Rev. D 48 (1993) 946 [INSPIRE].

    ADS  Google Scholar 

  84. K. Freese and W.H. Kinney, On: natural inflation, Phys. Rev. D 70 (2004) 083512 [hep-ph/0404012] [INSPIRE].

    ADS  Google Scholar 

  85. L. Sorbo, Parity violation in the cosmic microwave background from a pseudoscalar inflaton, JCAP 06 (2011) 003 [arXiv:1101.1525] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  88. J.M. Maldacena and G.L. Pimentel, On graviton non-gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].

    Article  ADS  Google Scholar 

  89. J. Soda, H. Kodama and M. Nozawa, Parity violation in graviton non-gaussianity, JHEP 08 (2011) 067 [arXiv:1106.3228] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  MATH  Google Scholar 

  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. 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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  94. K. Murata and J. Soda, Anisotropic inflation with non-abelian gauge kinetic function, JCAP 06 (2011) 037 [arXiv:1103.6164] [INSPIRE].

    Article  ADS  Google Scholar 

  95. A. Maleknejad and M. Sheikh-Jabbari, Gauge-flation: inflation from non-abelian gauge fields, arXiv:1102.1513 [INSPIRE].

  96. A. Maleknejad, M. Sheikh-Jabbari and J. Soda, Gauge-flation and cosmic no-hair conjecture, JCAP 01 (2012) 016 [arXiv:1109.5573] [INSPIRE].

    Article  ADS  Google Scholar 

  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. 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].

    Article  ADS  Google Scholar 

  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. 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].

    ADS  Google Scholar 

  101. D.H. Lyth, Primordial black hole formation and hybrid inflation, arXiv:1107.1681 [INSPIRE].

  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].

    ADS  Google Scholar 

  103. K. Dimopoulos, Inflation at the TeV scale with a PNGB curvaton, Phys. Lett. B 634 (2006) 331 [hep-th/0511268] [INSPIRE].

    Article  ADS  Google Scholar 

  104. K. Dimopoulos and G. Lazarides, Modular inflation and the orthogonal axion as curvaton, Phys. Rev. D 73 (2006) 023525 [hep-ph/0511310] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Consortium for Fundamental Physics, Physics Department, Lancaster University, Lancaster, LA1 4YB, UK

    Konstantinos Dimopoulos

  2. CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, 18071, Spain

    Mindaugas Karčiauskas

Authors
  1. Konstantinos Dimopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mindaugas Karčiauskas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mindaugas Karčiauskas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dimopoulos, K., Karčiauskas, M. Parity Violating Statistical Anisotropy. J. High Energ. Phys. 2012, 40 (2012). https://doi.org/10.1007/JHEP06(2012)040

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)040

Keywords

Search

Navigation