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Brane SUSY breaking and the gravitino mass

  • Noriaki Kitazawa
Open Access
Regular Article - Theoretical Physics
  • 53 Downloads

Abstract

Supergravity models with spontaneously broken supersymmetry have been widely investigated over the years, together with some notable non-linear limits. Although in these models the gravitino becomes naturally massive absorbing the degrees of freedom of a Nambu-Goldstone fermion, there are cases in which the naive counting of degrees of freedom does not apply, in particular because of the absence of explicit gravitino mass terms in unitary gauge. The corresponding models require non-trivial de Sitter-like backgrounds, and it becomes of interest to clarify the fate of their Nambu-Goldstone modes. We elaborate on the fact that these non-trivial backgrounds can accommodate, consistently, gravitino fields carrying a number of degrees of freedom that is intermediate between those of massless and massive fields in a flat spacetime. For instance, in a simple supergravity model of this type with de Sitter background, the overall degrees of freedom of gravitino are as many as for a massive spin-3/2 field in flat spacetime, while the gravitino remains massless in the sense that it undergoes null-cone propagation in the stereographic picture. On the other hand, in the ten-dimensional USp(32) Type I Sugimoto model with “brane SUSY breaking”, which requires a more complicated background, the degrees of freedom of gravitino are half as many of those of a massive one, and yet it somehow behaves again as a massless one.

Keywords

Supersymmetry Breaking D-branes Supergravity Models 

Notes

Open Access

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References

  1. [1]
    P. Ramond, Dual Theory for Free Fermions, Phys. Rev. D 3 (1971) 2415 [INSPIRE].ADSMathSciNetGoogle Scholar
  2. [2]
    Yu. A. Golfand and E.P. Likhtman, Extension of the Algebra of Poincaré Group Generators and Violation of p Invariance, JETP Lett. 13 (1971) 323 [Pisma Zh. Eksp. Teor. Fiz. 13 (1971) 452]. [INSPIRE].
  3. [3]
    J.-L. Gervais and B. Sakita, Field Theory Interpretation of Supergauges in Dual Models, Nucl. Phys. B 34 (1971) 632 [INSPIRE].
  4. [4]
    J. Wess and B. Zumino, A Lagrangian Model Invariant Under Supergauge Transformations, Phys. Lett. B 49 (1974) 52 [INSPIRE].
  5. [5]
    J. Wess and B. Zumino, Supergauge Transformations in Four-Dimensions, Nucl. Phys. B 70 (1974) 39 [INSPIRE].
  6. [6]
    A. Salam and J.A. Strathdee, Supergauge Transformations, Nucl. Phys. B 76 (1974) 477 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S. Ferrara and B. Zumino, Supergauge Invariant Yang-Mills Theories, Nucl. Phys. B 79 (1974) 413 [INSPIRE].
  8. [8]
    A. Salam and J.A. Strathdee, Supersymmetry and Nonabelian Gauges, Phys. Lett. B 51 (1974) 353 [INSPIRE].
  9. [9]
    P. Fayet and J. Iliopoulos, Spontaneously Broken Supergauge Symmetries and Goldstone Spinors, Phys. Lett. B 51 (1974) 461 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Progress Toward a Theory of Supergravity, Phys. Rev. D 13 (1976) 3214 [INSPIRE].
  11. [11]
    S. Deser and B. Zumino, Consistent Supergravity, Phys. Lett. B 62 (1976) 335 [INSPIRE].
  12. [12]
    D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).Google Scholar
  13. [13]
    P. Van Nieuwenhuizen, Supergravity, Phys. Rept. 68 (1981) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    S. Ferrara and A. Sagnotti, Supergravity at 40: Reflections and Perspectives, Riv. Nuovo Cim. 40 (2017) 1 [J. Phys. Conf. Ser. 873 (2017) 012014] [arXiv:1702.00743] [INSPIRE].
  15. [15]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory, 2 volumes, Cambridge University Press, Cambridge U.K. (1987).Google Scholar
  16. [16]
    J. Polchinski, String theory, 2 volumes, Cambridge University Press, Cambridge U.K. (1998).Google Scholar
  17. [17]
    C.V. Johnson, D-branes, Cambridge University Press, Cambridge U.K. (2003).Google Scholar
  18. [18]
    B. Zwiebach, A first course in string theory, Cambridge University Press, Cambridge U.K. (2004).Google Scholar
  19. [19]
    K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, Cambridge U.K. (2007).Google Scholar
  20. [20]
    E. Kiritsis, String theory in a nutshell, Cambridge University Press, Cambridge U.K. (2007).Google Scholar
  21. [21]
    P. West, Introduction to strings and branes, Cambridge University Press, Cambridge U.K. (2012).Google Scholar
  22. [22]
    D.V. Volkov and V.P. Akulov, Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    D.V. Volkov and V.A. Soroka, Higgs Effect for Goldstone Particles with Spin 1/2, JETP Lett. 18 (1973) 312 [Pisma Zh. Eksp. Teor. Fiz. 18 (1973) 529] [INSPIRE].
  24. [24]
    D.V. Volkov and V.A. Soroka, Gauge fields for symmetry group with spinor parameters, Theor. Math. Phys. 20 (1974) 829 [Teor. Mat. Fiz. 20 (1974) 291] [INSPIRE].
  25. [25]
    S. Deser and B. Zumino, Broken Supersymmetry and Supergravity, Phys. Rev. Lett. 38 (1977) 1433 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    E. Dudas, S. Ferrara, A. Kehagias and A. Sagnotti, Properties of Nilpotent Supergravity, JHEP 09 (2015) 217 [arXiv:1507.07842] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    F. Hasegawa and Y. Yamada, Component action of nilpotent multiplet coupled to matter in 4 dimensional \( \mathcal{N}=1 \) supergravity, JHEP 10 (2015) 106 [arXiv:1507.08619] [INSPIRE].
  28. [28]
    E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter Supergravity, Phys. Rev. D 92 (2015) 085040 [Erratum ibid. D 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
  29. [29]
    N. Cribiori, G. Dall’Agata and F. Farakos, From Linear to Non-linear SUSY and Back Again, JHEP 08 (2017) 117 [arXiv:1704.07387] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, Nonlinear Realization of Supersymmetry Algebra From Supersymmetric Constraint, Phys. Lett. B 220 (1989) 569 [INSPIRE].
  31. [31]
    A. Brignole, F. Feruglio and F. Zwirner, On the effective interactions of a light gravitino with matter fermions, JHEP 11 (1997) 001 [hep-th/9709111] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Z. Komargodski and N. Seiberg, From Linear SUSY to Constrained Superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    S.M. Kuzenko and S.J. Tyler, Relating the Komargodski-Seiberg and Akulov-Volkov actions: Exact nonlinear field redefinition, Phys. Lett. B 698 (2011) 319 [arXiv:1009.3298] [INSPIRE].
  34. [34]
    I. Bandos, L. Martucci, D. Sorokin and M. Tonin, Brane induced supersymmetry breaking and de Sitter supergravity, JHEP 02 (2016) 080 [arXiv:1511.03024] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    I. Bandos, M. Heller, S.M. Kuzenko, L. Martucci and D. Sorokin, The Goldstino brane, the constrained superfields and matter in \( \mathcal{N}=1 \) supergravity, JHEP 11 (2016) 109 [arXiv:1608.05908] [INSPIRE].
  36. [36]
    E. Cremmer, B. Julia, J. Scherk, S. Ferrara, L. Girardello and P. van Nieuwenhuizen, Spontaneous Symmetry Breaking and Higgs Effect in Supergravity Without Cosmological Constant, Nucl. Phys. B 147 (1979) 105 [INSPIRE].
  37. [37]
    A.H. Chamseddine, R.L. Arnowitt and P. Nath, Locally Supersymmetric Grand Unification, Phys. Rev. Lett. 49 (1982) 970 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    J. Bagger and E. Witten, The Gauge Invariant Supersymmetric Nonlinear σ-model, Phys. Lett. B 118 (1982) 103 [INSPIRE].
  39. [39]
    E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
  40. [40]
    E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally Vanishing Cosmological Constant in N = 1 Supergravity, Phys. Lett. B 133 (1983) 61 [INSPIRE].
  41. [41]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
  42. [42]
    A. Sagnotti, Open Strings and their Symmetry Groups, in Cargese ’87, Non-Perturbative Quantum Field Theory, G. Mack et al. eds., Pergamon Press (1988), p. 521 [hep-th/0208020] [INSPIRE].
  43. [43]
    G. Pradisi and A. Sagnotti, Open String Orbifolds, Phys. Lett. B 216 (1989) 59 [INSPIRE].
  44. [44]
    P. Hořava, Strings on World Sheet Orbifolds, Nucl. Phys. B 327 (1989) 461 [INSPIRE].
  45. [45]
    P. Hořava, Background Duality of Open String Models, Phys. Lett. B 231 (1989) 251 [INSPIRE].
  46. [46]
    M. Bianchi and A. Sagnotti, On the systematics of open string theories, Phys. Lett. B 247 (1990) 517 [INSPIRE].
  47. [47]
    M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys. B 361 (1991) 519 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    M. Bianchi, G. Pradisi and A. Sagnotti, Toroidal compactification and symmetry breaking in open string theories, Nucl. Phys. B 376 (1992) 365 [INSPIRE].
  49. [49]
    A. Sagnotti, A Note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
  50. [50]
    E. Dudas, Theory and phenomenology of type-I strings and M-theory, Class. Quant. Grav. 17 (2000) R41 [hep-ph/0006190] [INSPIRE].
  51. [51]
    C. Angelantonj and A. Sagnotti, Open strings, Phys. Rept. 371 (2002) 1 [Erratum ibid. 376 (2003) 339] [hep-th/0204089] [INSPIRE].
  52. [52]
    S. Sugimoto, Anomaly cancellations in type-I D-9- \( \overline{D}-9 \) system and the USp(32) string theory, Prog. Theor. Phys. 102 (1999) 685 [hep-th/9905159] [INSPIRE].
  53. [53]
    I. Antoniadis, E. Dudas and A. Sagnotti, Brane supersymmetry breaking, Phys. Lett. B 464 (1999) 38 [hep-th/9908023] [INSPIRE].
  54. [54]
    C. Angelantonj, Comments on open string orbifolds with a nonvanishing B(ab), Nucl. Phys. B 566 (2000) 126 [hep-th/9908064] [INSPIRE].
  55. [55]
    G. Aldazabal and A.M. Uranga, Tachyon free nonsupersymmetric type IIB orientifolds via Brane - anti-brane systems, JHEP 10 (1999) 024 [hep-th/9908072] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  56. [56]
    C. Angelantonj, I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti, Type I vacua with brane supersymmetry breaking, Nucl. Phys. B 572 (2000) 36 [hep-th/9911081] [INSPIRE].
  57. [57]
    J. Mourad and A. Sagnotti, An Update on Brane Supersymmetry Breaking, arXiv:1711.11494 [INSPIRE].
  58. [58]
    E. Dudas and J. Mourad, Consistent gravitino couplings in nonsupersymmetric strings, Phys. Lett. B 514 (2001) 173 [hep-th/0012071] [INSPIRE].
  59. [59]
    G. Pradisi and F. Riccioni, Geometric couplings and brane supersymmetry breaking, Nucl. Phys. B 615 (2001) 33 [hep-th/0107090] [INSPIRE].
  60. [60]
    E. Dudas and J. Mourad, Brane solutions in strings with broken supersymmetry and dilaton tadpoles, Phys. Lett. B 486 (2000) 172 [hep-th/0004165] [INSPIRE].
  61. [61]
    R. Blumenhagen and A. Font, Dilaton tadpoles, warped geometries and large extra dimensions for nonsupersymmetric strings, Nucl. Phys. B 599 (2001) 241 [hep-th/0011269] [INSPIRE].
  62. [62]
    S. Deser and R.I. Nepomechie, Gauge Invariance Versus Masslessness in de Sitter Space, Annals Phys. 154 (1984) 396 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    S. Deser and A. Waldron, Null propagation of partially massless higher spins in (A)dS and cosmological constant speculations, Phys. Lett. B 513 (2001) 137 [hep-th/0105181] [INSPIRE].
  64. [64]
    S. Deser and A. Waldron, Gauge invariances and phases of massive higher spins in (A)dS, Phys. Rev. Lett. 87 (2001) 031601 [hep-th/0102166] [INSPIRE].
  65. [65]
    T. Garidi, What is mass in de Sitterian physics?, hep-th/0309104 [INSPIRE].
  66. [66]
    S. Deser and A. Waldron, Conformal invariance of partially massless higher spins, Phys. Lett. B 603 (2004) 30 [hep-th/0408155] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  67. [67]
    F. Gursey and T.D. Lee, Spin 1/2 Wave Equation in de Sitter Space, Proc. Nat. Acad. Sci. 49 (1963) 179 [INSPIRE].
  68. [68]
    Y. Tanii, Introduction to supergravity, SpringerBriefs in Mathematical Physics (2014).Google Scholar
  69. [69]
    D.Z. Freedman, Supergravity with Axial Gauge Invariance, Phys. Rev. D 15 (1977) 1173 [INSPIRE].
  70. [70]
    B. Zumino, Nonlinear Realization of Supersymmetry in de Sitter Space, Nucl. Phys. B 127 (1977) 189 [INSPIRE].
  71. [71]
    S. Ferrara and A. Van Proeyen, Mass Formulae for Broken Supersymmetry in Curved Space-Time, Fortsch. Phys. 64 (2016) 896 [arXiv:1609.08480] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  72. [72]
    A.O. Barut and B.-W. Xu, Conformal Covariance and the Probability Interpretation of Wave Equations, Phys. Lett. A 82 (1981) 218 [INSPIRE].
  73. [73]
    S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [INSPIRE].
  74. [74]
    J.G. Russo, Exact solution of scalar tensor cosmology with exponential potentials and transient acceleration, Phys. Lett. B 600 (2004) 185 [hep-th/0403010] [INSPIRE].
  75. [75]
    E. Dudas, N. Kitazawa and A. Sagnotti, On Climbing Scalars in String Theory, Phys. Lett. B 694 (2011) 80 [arXiv:1009.0874] [INSPIRE].
  76. [76]
    A. Sagnotti, Brane SUSY breaking and inflation: implications for scalar fields and CMB distortion, Phys. Part. Nucl. Lett. 11 (2014) 836 [arXiv:1303.6685] [INSPIRE].CrossRefGoogle Scholar
  77. [77]
    P. Fré, A. Sagnotti and A.S. Sorin, Integrable Scalar Cosmologies I. Foundations and links with String Theory, Nucl. Phys. B 877 (2013) 1028 [arXiv:1307.1910] [INSPIRE].
  78. [78]
    C. Condeescu and E. Dudas, Kasner solutions, climbing scalars and big-bang singularity, JCAP 08 (2013) 013 [arXiv:1306.0911] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  79. [79]
    A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
  80. [80]
    D. Kazanas, Dynamics of the Universe and Spontaneous Symmetry Breaking, Astrophys. J. 241 (1980) L59 [INSPIRE].
  81. [81]
    K. Sato, Cosmological Baryon Number Domain Structure and the First Order Phase Transition of a Vacuum, Phys. Lett. B 99 (1981) 66 [INSPIRE].
  82. [82]
    A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
  83. [83]
    A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].
  84. [84]
    A. Albrecht and P.J. Steinhardt, Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].ADSCrossRefGoogle Scholar
  85. [85]
    A.D. Linde, Chaotic Inflation, Phys. Lett. B 129 (1983) 177 [INSPIRE].
  86. [86]
    N. Bartolo, E. Komatsu, S. Matarrese and A. Riotto, Non-Gaussianity from inflation: Theory and observations, Phys. Rept. 402 (2004) 103 [astro-ph/0406398] [INSPIRE].
  87. [87]
    V. Mukhanov, Physical foundations of cosmology, Cambridge University Press, Cambridge U.K. (2005).Google Scholar
  88. [88]
    S. Weinberg, Cosmology, Cambridge University Press, Cambridge U.K. (2008).Google Scholar
  89. [89]
    D.H. Lyth and A.R. Liddle, The primordial density perturbation: Cosmology, inflation and the origin of structure, Cambridge University Press, Cambridge U.K. (2009).Google Scholar
  90. [90]
    D.S. Gorbunov and V.A. Rubakov, Introduction to the theory of the early universe: Cosmological perturbations and inflationary theory, World Scientific, Hackensack U.S.A. (2011).Google Scholar
  91. [91]
    J. Martin, C. Ringeval and V. Vennin, Encyclopædia Inflationaris, Phys. Dark Univ. 5-6 (2014) 75 [arXiv:1303.3787] [INSPIRE].
  92. [92]
    A.D. Linde, A Toy model for open inflation, Phys. Rev. D 59 (1999) 023503 [hep-ph/9807493] [INSPIRE].
  93. [93]
    C.R. Contaldi, M. Peloso, L. Kofman and A.D. Linde, Suppressing the lower multipoles in the CMB anisotropies, JCAP 07 (2003) 002 [astro-ph/0303636] [INSPIRE].
  94. [94]
    Y.-S. Piao, B. Feng and X.-m. Zhang, Suppressing CMB quadrupole with a bounce from contracting phase to inflation, Phys. Rev. D 69 (2004) 103520 [hep-th/0310206] [INSPIRE].
  95. [95]
    Y.-S. Piao, A Possible explanation to low CMB quadrupole, Phys. Rev. D 71 (2005) 087301 [astro-ph/0502343] [INSPIRE].
  96. [96]
    D. Boyanovsky, H.J. de Vega and N.G. Sanchez, CMB quadrupole suppression. 2. The early fast roll stage, Phys. Rev. D 74 (2006) 123007 [astro-ph/0607487] [INSPIRE].
  97. [97]
    C. Destri, H.J. de Vega and N.G. Sanchez, The CMB Quadrupole depression produced by early fast-roll inflation: MCMC analysis of WMAP and SDSS data, Phys. Rev. D 78 (2008) 023013 [arXiv:0804.2387] [INSPIRE].
  98. [98]
    F.J. Cao, H.J. de Vega and N.G. Sanchez, Quantum slow-roll and quantum fast-roll inflationary initial conditions: CMB quadrupole suppression and further effects on the low CMB multipoles, Phys. Rev. D 78 (2008) 083508 [arXiv:0809.0623] [INSPIRE].
  99. [99]
    R.K. Jain, P. Chingangbam, J.-O. Gong, L. Sriramkumar and T. Souradeep, Punctuated inflation and the low CMB multipoles, JCAP 01 (2009) 009 [arXiv:0809.3915] [INSPIRE].ADSCrossRefGoogle Scholar
  100. [100]
    E. Ramirez and D.J. Schwarz, ϕ 4 inflation is not excluded, Phys. Rev. D 80 (2009) 023525 [arXiv:0903.3543] [INSPIRE].
  101. [101]
    E. Ramirez and D.J. Schwarz, Predictions of just-enough inflation, Phys. Rev. D 85 (2012) 103516 [arXiv:1111.7131] [INSPIRE].
  102. [102]
    R.K. Jain, P. Chingangbam, L. Sriramkumar and T. Souradeep, The tensor-to-scalar ratio in punctuated inflation, Phys. Rev. D 82 (2010) 023509 [arXiv:0904.2518] [INSPIRE].
  103. [103]
    C. Destri, H.J. de Vega and N.G. Sanchez, The pre-inflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles, Phys. Rev. D 81 (2010) 063520 [arXiv:0912.2994] [INSPIRE].
  104. [104]
    E. Ramirez, Low power on large scales in just enough inflation models, Phys. Rev. D 85 (2012) 103517 [arXiv:1202.0698] [INSPIRE].
  105. [105]
    Z.-G. Liu, Z.-K. Guo and Y.-S. Piao, Obtaining the CMB anomalies with a bounce from the contracting phase to inflation, Phys. Rev. D 88 (2013) 063539 [arXiv:1304.6527] [INSPIRE].
  106. [106]
    F.G. Pedro and A. Westphal, Low-CMB power loss in string inflation, JHEP 04 (2014) 034 [arXiv:1309.3413] [INSPIRE].ADSCrossRefGoogle Scholar
  107. [107]
    M. Cicoli, S. Downes, B. Dutta, F.G. Pedro and A. Westphal, Just enough inflation: power spectrum modifications at large scales, JCAP 12 (2014) 030 [arXiv:1407.1048] [INSPIRE].ADSCrossRefGoogle Scholar
  108. [108]
    R. Bousso, D. Harlow and L. Senatore, Inflation after False Vacuum Decay, Phys. Rev. D 91 (2015) 083527 [arXiv:1309.4060] [INSPIRE].
  109. [109]
    Z.-G. Liu, Z.-K. Guo and Y.-S. Piao, CMB anomalies from an inflationary model in string theory, Eur. Phys. J. C 74 (2014) 3006 [arXiv:1311.1599] [INSPIRE].
  110. [110]
    A.Y. Kamenshchik, A. Tronconi and G. Venturi, Quantum Gravity and the Large Scale Anomaly, JCAP 04 (2015) 046 [arXiv:1501.06404] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  111. [111]
    Y.-F. Cai, E.G.M. Ferreira, B. Hu and J. Quintin, Searching for features of a string-inspired inflationary model with cosmological observations, Phys. Rev. D 92 (2015) 121303 [arXiv:1507.05619] [INSPIRE].
  112. [112]
    E. Dudas, N. Kitazawa, S.P. Patil and A. Sagnotti, CMB Imprints of a Pre-Inflationary Climbing Phase, JCAP 05 (2012) 012 [arXiv:1202.6630] [INSPIRE].ADSCrossRefGoogle Scholar
  113. [113]
    A. Gruppuso and A. Sagnotti, Observational Hints of a Pre-Inflationary Scale?, Int. J. Mod. Phys. D 24 (2015) 1544008 [arXiv:1506.08093] [INSPIRE].
  114. [114]
    A. Gruppuso, N. Kitazawa, N. Mandolesi, P. Natoli and A. Sagnotti, Pre-Inflationary Relics in the CMB?, Phys. Dark Univ. 11 (2016) 68 [arXiv:1508.00411] [INSPIRE].CrossRefGoogle Scholar
  115. [115]
    A. Gruppuso, N. Kitazawa, M. Lattanzi, N. Mandolesi, P. Natoli and A. Sagnotti, The Evens and Odds of CMB Anomalies, Phys. Dark Univ. 20 (2018) 49 [arXiv:1712.03288] [INSPIRE].CrossRefGoogle Scholar
  116. [116]
    A. Kehagias and A. Riotto, On the Inflationary Perturbations of Massive Higher-Spin Fields, JCAP 07 (2017) 046 [arXiv:1705.05834] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  117. [117]
    N. Bartolo, A. Kehagias, M. Liguori, A. Riotto, M. Shiraishi and V. Tansella, Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra, Phys. Rev. D 97 (2018) 023503 [arXiv:1709.05695] [INSPIRE].
  118. [118]
    D. Baumann, G. Goon, H. Lee and G.L. Pimentel, Partially Massless Fields During Inflation, arXiv:1712.06624 [INSPIRE].
  119. [119]
    G. Franciolini, A. Kehagias and A. Riotto, Imprints of Spinning Particles on Primordial Cosmological Perturbations, JCAP 02 (2018) 023 [arXiv:1712.06626] [INSPIRE].ADSCrossRefGoogle Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsTokyo Metropolitan UniversityHachiojiJapan

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