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Journal of High Energy Physics

, 2011:45 | Cite as

On graviton non-gaussianities during inflation

  • Juan M. Maldacena
  • Guilherme L. Pimentel
Article

Abstract

We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum [1, 2], even though it is present in the wavefunction. We also introduce a spinor helicity formalism to describe de Sitter gravitational waves with circular polarization.

These results also apply to correlation functions in Anti-de Sitter space. They also describe the general form of stress tensor correlation functions, in momentum space, in a three dimensional conformal field theory. Here all three shapes can arise, including the parity violating one.

Keywords

Gauge-gravity correspondence AdS-CFT Correspondence Models of Quantum Gravity Conformal and W Symmetry 

References

  1. [1]
    J. Soda, H. Kodama and M. Nozawa, Parity violation in graviton non-Gaussianity, JHEP 08 (2011) 067 [arXiv:1106.3228] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    M. Shiraishi, D. Nitta and S. Yokoyama, Parity violation of gravitons in the CMB bispectrum, arXiv:1108.0175 [SPIRES].
  3. [3]
    C. Cheung, P. Creminelli, A.L. Fitzpatrick, J. Kaplan and L. Senatore, The effective field theory of inflation, JHEP 03 (2008) 014 [arXiv:0709.0293] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    C. Cheung, A.L. Fitzpatrick, J. Kaplan and L. Senatore, On the consistency relation of the 3-point function in single field inflation, JCAP 02 (2008) 021 [arXiv:0709.0295] [SPIRES].ADSGoogle Scholar
  5. [5]
    X. Chen, M.-x. Huang, S. Kachru and G. Shiu, Observational signatures and non-Gaussianities of general single field inflation, JCAP 01 (2007) 002 [hep-th/0605045] [SPIRES].ADSGoogle Scholar
  6. [6]
    S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [SPIRES].ADSMathSciNetGoogle Scholar
  7. [7]
    G. Arutyunov and S. Frolov, Three-point Green function of the stress-energy tensor in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 026004 [hep-th/9901121] [SPIRES].ADSMathSciNetGoogle Scholar
  8. [8]
    J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [SPIRES].
  10. [10]
    M. Alishahiha, E. Silverstein and D. Tong, DBI in the sky, Phys. Rev. D 70 (2004) 123505 [hep-th/0404084] [SPIRES].ADSGoogle Scholar
  11. [11]
    C. Armendariz-Picon, T. Damour and V.F. Mukhanov, k-inflation, Phys. Lett. B 458 (1999) 209 [hep-th/9904075] [SPIRES].ADSMathSciNetGoogle Scholar
  12. [12]
    J. Garriga and V.F. Mukhanov, Perturbations in k-inflation, Phys. Lett. B 458 (1999) 219 [hep-th/9904176] [SPIRES].ADSMathSciNetGoogle Scholar
  13. [13]
    E. Silverstein and D. Tong, Scalar speed limits and cosmology: acceleration from D-cceleration, Phys. Rev. D 70 (2004) 103505 [hep-th/0310221] [SPIRES].ADSMathSciNetGoogle Scholar
  14. [14]
    L. Senatore and M. Zaldarriaga, The effective field theory of multifield inflation, arXiv:1009.2093 [SPIRES].
  15. [15]
    A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [SPIRES].
  17. [17]
    H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Ann. Phys. 231 (1994) 311 [hep-th/9307010] [SPIRES].CrossRefMATHADSMathSciNetGoogle Scholar
  18. [18]
    F. Larsen, J.P. vander Schaar and R.G. Leigh, De Sitter holography and the Cosmic Microwave Background, JHEP 04 (2002) 047 [hep-th/0202127] [SPIRES].CrossRefADSGoogle Scholar
  19. [19]
    F. Larsen and R. McNees, Inflation and de Sitter holography, JHEP 07 (2003) 051 [hep-th/0307026] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  20. [20]
    F. Larsen and R. McNees, Holography, diffeomorphisms and scaling violations in the CMB, JHEP 07 (2004) 062 [hep-th/0402050] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  21. [21]
    P. McFadden and K. Skenderis, Holography for cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [SPIRES].ADSMathSciNetGoogle Scholar
  22. [22]
    P. McFadden and K. Skenderis, Holographic non-Gaussianity, JCAP 05 (2011) 013 [arXiv:1011.0452] [SPIRES].ADSGoogle Scholar
  23. [23]
    I. Antoniadis, P.O. Mazur and E. Mottola, Conformal invariance, dark energy and CMB non-Gaussianity, arXiv:1103.4164 [SPIRES].
  24. [24]
    A.A. Starobinsky, Spectrum of relict gravitational radiation and the early state of the universe, JET P Lett. 30 (1979) 682 [Pisma Zh. Eksp. Teor. Fiz. 30 (1979) 719] [SPIRES].ADSGoogle Scholar
  25. [25]
    T.S. Bunch and P.C.W. Davies, Quantum Field Theory In de Sitter space: renormalization by point splitting, Proc. Roy. Soc. Lond. A 360 (1978) 117 [SPIRES].ADSMathSciNetGoogle Scholar
  26. [26]
    A. Lue, L.-M. Wang and M. Kamionkowski, Cosmological signature of new parity-violating interactions, Phys. Rev. Lett. 83 (1999) 1506 [astro-ph/9812088] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    S. Alexander and J. Martin, Birefringent gravitational waves and the consistency check of inflation, Phys. Rev. D 71 (2005) 063526 [hep-th/0410230] [SPIRES].ADSGoogle Scholar
  28. [28]
    C.R. Contaldi, J. Magueijo and L. Smolin, Anomalous CMB polarization and gravitational chirality, Phys. Rev. Lett. 101 (2008) 141101 [arXiv:0806.3082] [SPIRES].CrossRefADSGoogle Scholar
  29. [29]
    D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [SPIRES].CrossRefADSGoogle Scholar
  30. [30]
    M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity bound violation in higher derivative gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [SPIRES].ADSGoogle Scholar
  31. [31]
    M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The viscosity bound and causality violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    D.M. Hofman, Higher derivative gravity, causality and positivity of energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  33. [33]
    N. Kaloper, M. Kleban, A.E. Lawrence and S. Shenker, Signatures of short distance physics in the Cosmic Microwave Background, Phys. Rev. D 66 (2002) 123510 [hep-th/0201158] [SPIRES].ADSGoogle Scholar
  34. [34]
    E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].CrossRefMATHADSMathSciNetGoogle Scholar
  35. [35]
    N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  36. [36]
    C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, JHEP 07 (2009) 075 [arXiv:0902.0981] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  37. [37]
    J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [SPIRES].CrossRefGoogle Scholar
  38. [38]
    A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [SPIRES].CrossRefADSGoogle Scholar
  39. [39]
    M.T. Grisaru and H.N. Pendleton, Some properties of scattering amplitudes in supersymmetric theories, Nucl. Phys. B 124 (1977) 81 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  40. [40]
    S. Raju, BCFW for Witten diagrams, Phys. Rev. Lett. 106 (2011) 091601 [arXiv:1011.0780] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  41. [41]
    S. Raju, Recursion relations for AdS/CFT correlators, Phys. Rev. D 83 (2011) 126002 [arXiv:1102.4724] [SPIRES].ADSGoogle Scholar
  42. [42]
    F. Bastianelli, S. Frolov and A.A. Tseytlin, Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in D = 3 and D = 6, Nucl. Phys. B 578 (2000) 139 [hep-th/9911135] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  43. [43]
    S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  44. [44]
    S. Giombi and X. Yin, Higher spins in AdS and twistorial holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  45. [45]
    P.A.M. Dirac, Wave equations in conformal space, Annals Math. 37 (1936) 429 [SPIRES].CrossRefMathSciNetGoogle Scholar
  46. [46]
    S. Ferrara, A.F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  47. [47]
    S. Weinberg, Six-dimensional methods for four-dimensional conformal field theories, Phys. Rev. D 82 (2010) 045031 [arXiv:1006.3480] [SPIRES].ADSGoogle Scholar
  48. [48]
    E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  2. 2.Department of PhysicsPrinceton UniversityPrincetonU.S.A.

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