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.
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References
J. Soda, H. Kodama and M. Nozawa, Parity violation in graviton non-Gaussianity, JHEP 08 (2011) 067 [arXiv:1106.3228] [SPIRES].
M. Shiraishi, D. Nitta and S. Yokoyama, Parity violation of gravitons in the CMB bispectrum, arXiv:1108.0175 [SPIRES].
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].
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].
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].
S. Weinberg, Effective field theory for inflation, Phys. Rev. D 77 (2008) 123541 [arXiv:0804.4291] [SPIRES].
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].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [SPIRES].
P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [SPIRES].
M. Alishahiha, E. Silverstein and D. Tong, DBI in the sky, Phys. Rev. D 70 (2004) 123505 [hep-th/0404084] [SPIRES].
C. Armendariz-Picon, T. Damour and V.F. Mukhanov, k-inflation, Phys. Lett. B 458 (1999) 209 [hep-th/9904075] [SPIRES].
J. Garriga and V.F. Mukhanov, Perturbations in k-inflation, Phys. Lett. B 458 (1999) 219 [hep-th/9904176] [SPIRES].
E. Silverstein and D. Tong, Scalar speed limits and cosmology: acceleration from D-cceleration, Phys. Rev. D 70 (2004) 103505 [hep-th/0310221] [SPIRES].
L. Senatore and M. Zaldarriaga, The effective field theory of multifield inflation, arXiv:1009.2093 [SPIRES].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [SPIRES].
E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [SPIRES].
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].
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].
F. Larsen and R. McNees, Inflation and de Sitter holography, JHEP 07 (2003) 051 [hep-th/0307026] [SPIRES].
F. Larsen and R. McNees, Holography, diffeomorphisms and scaling violations in the CMB, JHEP 07 (2004) 062 [hep-th/0402050] [SPIRES].
P. McFadden and K. Skenderis, Holography for cosmology, Phys. Rev. D 81 (2010) 021301 [arXiv:0907.5542] [SPIRES].
P. McFadden and K. Skenderis, Holographic non-Gaussianity, JCAP 05 (2011) 013 [arXiv:1011.0452] [SPIRES].
I. Antoniadis, P.O. Mazur and E. Mottola, Conformal invariance, dark energy and CMB non-Gaussianity, arXiv:1103.4164 [SPIRES].
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].
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].
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].
S. Alexander and J. Martin, Birefringent gravitational waves and the consistency check of inflation, Phys. Rev. D 71 (2005) 063526 [hep-th/0410230] [SPIRES].
C.R. Contaldi, J. Magueijo and L. Smolin, Anomalous CMB polarization and gravitational chirality, Phys. Rev. Lett. 101 (2008) 141101 [arXiv:0806.3082] [SPIRES].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [SPIRES].
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].
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].
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].
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].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [SPIRES].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].
C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, JHEP 07 (2009) 075 [arXiv:0902.0981] [SPIRES].
J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [SPIRES].
A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [SPIRES].
M.T. Grisaru and H.N. Pendleton, Some properties of scattering amplitudes in supersymmetric theories, Nucl. Phys. B 124 (1977) 81 [SPIRES].
S. Raju, BCFW for Witten diagrams, Phys. Rev. Lett. 106 (2011) 091601 [arXiv:1011.0780] [SPIRES].
S. Raju, Recursion relations for AdS/CFT correlators, Phys. Rev. D 83 (2011) 126002 [arXiv:1102.4724] [SPIRES].
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].
S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [SPIRES].
S. Giombi and X. Yin, Higher spins in AdS and twistorial holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [SPIRES].
P.A.M. Dirac, Wave equations in conformal space, Annals Math. 37 (1936) 429 [SPIRES].
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].
S. Weinberg, Six-dimensional methods for four-dimensional conformal field theories, Phys. Rev. D 82 (2010) 045031 [arXiv:1006.3480] [SPIRES].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [SPIRES].
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ArXiv ePrint: 1104.2846
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Maldacena, J.M., Pimentel, G.L. On graviton non-gaussianities during inflation. J. High Energ. Phys. 2011, 45 (2011). https://doi.org/10.1007/JHEP09(2011)045
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DOI: https://doi.org/10.1007/JHEP09(2011)045