Abstract
We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders in derivatives. Working in perturbation theory, we construct all cubic interactions that can contribute to tree-level graviton bispectra, showing that they all come from EFToI operators containing two or three powers of the extrinsic curvature and its covariant derivatives: all other operators can be removed by field redefinitions or start at higher-order in perturbations. For operators cubic in the extrinsic curvature, where the single-clock consistency relations are satisfied without a correction to the graviton two-point function, we use the Manifestly Local Test (MLT) to efficiently extract the effects of evolving graviton fluctuations to the end of inflation. Despite the somewhat complicated nature of the bulk interactions, the final boundary correlators take a very compact form. For operators quadratic in the extrinsic curvature, the leading order bispectra are a sum of contact and single exchange diagrams, which are tied together by spatial diffeomorphisms, and to all orders in derivatives we derive these bispectra by computing the necessary bulk time integrals. For single exchange diagrams we exploit factorisation properties of the bulk-bulk propagator for massless gravitons and write the result as a finite sum over residues. Perhaps surprisingly, we show these single exchange contributions have only total-energy poles and also satisfy the MLT.
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References
J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
J. Soda, H. Kodama and M. Nozawa, Parity Violation in Graviton Non-Gaussianity, JHEP 08 (2011) 067 [arXiv:1106.3228] [INSPIRE].
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].
P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming Tree Amplitudes In General Relativity, JHEP 11 (2007) 057 [hep-th/0702032] [INSPIRE].
C. Cheung, TASI Lectures on Scattering Amplitudes, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: Anticipating the Next Discoveries in Particle Physics (TASI 2016), Boulder, CO, U.S.A., June 6–July 1, 2016, R. Essig and I. Low eds., pp. 571–623 (2018) [DOI] [arXiv:1708.03872] [INSPIRE].
P. Benincasa and F. Cachazo, Consistency Conditions on the S-matrix of Massless Particles, arXiv:0705.4305 [INSPIRE].
E. Pajer, D. Stefanyszyn and J. Supeł, The Boostless Bootstrap: Amplitudes without Lorentz boosts, JHEP 12 (2020) 198 [Erratum ibid. 04 (2022) 023] [arXiv:2007.00027] [INSPIRE].
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] [INSPIRE].
P. Creminelli, J. Gleyzes, J. Noreña and F. Vernizzi, Resilience of the standard predictions for primordial tensor modes, Phys. Rev. Lett. 113 (2014) 231301 [arXiv:1407.8439] [INSPIRE].
L. Bordin, G. Cabass, P. Creminelli and F. Vernizzi, Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings, JCAP 09 (2017) 043 [arXiv:1706.03758] [INSPIRE].
L. Bordin and G. Cabass, Graviton non-Gaussianities and Parity Violation in the EFT of Inflation, JCAP 07 (2020) 014 [arXiv:2004.00619] [INSPIRE].
G. Cabass, E. Pajer, D. Stefanyszyn and J. Supeł, Bootstrapping large graviton non-Gaussianities, JHEP 05 (2022) 077 [arXiv:2109.10189] [INSPIRE].
S. Endlich, A. Nicolis and J. Wang, Solid Inflation, JCAP 10 (2013) 011 [arXiv:1210.0569] [INSPIRE].
G. Cabass, Zoology of graviton non-Gaussianities, JCAP 12 (2021) 001 [arXiv:2103.09816] [INSPIRE].
K. Hinterbichler, L. Hui and J. Khoury, An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology, JCAP 01 (2014) 039 [arXiv:1304.5527] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
P. Creminelli, J. Noreña and M. Simonović, Conformal consistency relations for single-field inflation, JCAP 07 (2012) 052 [arXiv:1203.4595] [INSPIRE].
K. Hinterbichler, L. Hui and J. Khoury, Conformal Symmetries of Adiabatic Modes in Cosmology, JCAP 08 (2012) 017 [arXiv:1203.6351] [INSPIRE].
N. Bartolo and G. Orlando, Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves, JCAP 07 (2017) 034 [arXiv:1706.04627] [INSPIRE].
N. Bartolo, L. Caloni, G. Orlando and A. Ricciardone, Tensor non-Gaussianity in chiral scalar-tensor theories of gravity, JCAP 03 (2021) 073 [arXiv:2008.01715] [INSPIRE].
G. Orlando, Probing parity-odd bispectra with anisotropies of GW V modes, arXiv:2206.14173 [INSPIRE].
G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Shapes of gravity: Tensor non-Gaussianity and massive spin-2 fields, JHEP 10 (2019) 182 [arXiv:1812.07571] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
D. Stefanyszyn and J. Supeł, The Boostless Bootstrap and BCFW Momentum Shifts, JHEP 03 (2021) 091 [arXiv:2009.14289] [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
H. Goodhew, S. Jazayeri and E. Pajer, The Cosmological Optical Theorem, JCAP 04 (2021) 021 [arXiv:2009.02898] [INSPIRE].
S. Melville and E. Pajer, Cosmological Cutting Rules, JHEP 05 (2021) 249 [arXiv:2103.09832] [INSPIRE].
H. Goodhew, S. Jazayeri, M.H. Gordon Lee and E. Pajer, Cutting cosmological correlators, JCAP 08 (2021) 003 [arXiv:2104.06587] [INSPIRE].
S. Céspedes, A.-C. Davis and S. Melville, On the time evolution of cosmological correlators, JHEP 02 (2021) 012 [arXiv:2009.07874] [INSPIRE].
S. Jazayeri, E. Pajer and D. Stefanyszyn, From locality and unitarity to cosmological correlators, JHEP 10 (2021) 065 [arXiv:2103.08649] [INSPIRE].
D. Baumann, W.-M. Chen, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, Linking the singularities of cosmological correlators, JHEP 09 (2022) 010 [arXiv:2106.05294] [INSPIRE].
D. Meltzer, The inflationary wavefunction from analyticity and factorization, JCAP 12 (2021) 018 [arXiv:2107.10266] [INSPIRE].
H. Gomez, R.L. Jusinskas and A. Lipstein, Cosmological Scattering Equations, Phys. Rev. Lett. 127 (2021) 251604 [arXiv:2106.11903] [INSPIRE].
C. Sleight and M. Taronna, From dS to AdS and back, JHEP 12 (2021) 074 [arXiv:2109.02725] [INSPIRE].
L. Di Pietro, V. Gorbenko and S. Komatsu, Analyticity and unitarity for cosmological correlators, JHEP 03 (2022) 023 [arXiv:2108.01695] [INSPIRE].
M. Hogervorst, J. Penedones and K.S. Vaziri, Towards the non-perturbative cosmological bootstrap, arXiv:2107.13871 [INSPIRE].
N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities, JHEP 04 (2020) 105 [arXiv:1811.00024] [INSPIRE].
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, The cosmological bootstrap: weight-shifting operators and scalar seeds, JHEP 12 (2020) 204 [arXiv:1910.14051] [INSPIRE].
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization, SciPost Phys. 11 (2021) 071 [arXiv:2005.04234] [INSPIRE].
J. Bonifacio, E. Pajer and D.-G. Wang, From amplitudes to contact cosmological correlators, JHEP 10 (2021) 001 [arXiv:2106.15468] [INSPIRE].
E. Pajer, Building a Boostless Bootstrap for the Bispectrum, JCAP 01 (2021) 023 [arXiv:2010.12818] [INSPIRE].
P. Benincasa, Cosmological Polytopes and the Wavefuncton of the Universe for Light States, arXiv:1909.02517 [INSPIRE].
P. Benincasa, From the flat-space S-matrix to the Wavefunction of the Universe, arXiv:1811.02515 [INSPIRE].
N. Arkani-Hamed, P. Benincasa and A. Postnikov, Cosmological Polytopes and the Wavefunction of the Universe, arXiv:1709.02813 [INSPIRE].
D. Green and E. Pajer, On the Symmetries of Cosmological Perturbations, JCAP 09 (2020) 032 [arXiv:2004.09587] [INSPIRE].
C. Sleight and M. Taronna, On the consistency of (partially-)massless matter couplings in de Sitter space, JHEP 10 (2021) 156 [arXiv:2106.00366] [INSPIRE].
C. Sleight and M. Taronna, From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing, Phys. Rev. D 104 (2021) L081902 [arXiv:2007.09993] [INSPIRE].
C. Sleight and M. Taronna, Bootstrapping Inflationary Correlators in Mellin Space, JHEP 02 (2020) 098 [arXiv:1907.01143] [INSPIRE].
C. Sleight, A Mellin Space Approach to Cosmological Correlators, JHEP 01 (2020) 090 [arXiv:1906.12302] [INSPIRE].
A. Hillman, Symbol Recursion for the dS Wave Function, arXiv:1912.09450 [INSPIRE].
N. Bittermann and A. Joyce, Soft limits of the wavefunction in exceptional scalar theories, arXiv:2203.05576 [INSPIRE].
P. Benincasa and W.J.T. Bobadilla, Physical representations for scattering amplitudes and the wavefunction of the universe, SciPost Phys. 12 (2022) 192 [arXiv:2112.09028] [INSPIRE].
D. Baumann et al., Snowmass White Paper: The Cosmological Bootstrap, in 2022 Snowmass Summer Study, (2022) [arXiv:2203.08121] [INSPIRE].
P. Benincasa, Amplitudes meet Cosmology: A (Scalar) Primer, arXiv:2203.15330 [INSPIRE].
P. Benincasa, Wavefunctionals/S-matrix techniques in de Sitter, in 21st Hellenic School and Workshops on Elementary Particle Physics and Gravity, (2022) [arXiv:2203.16378] [INSPIRE].
C. Armstrong, H. Gomez, R. Lipinski Jusinskas, A. Lipstein and J. Mei, Effective field theories and cosmological scattering equations, JHEP 08 (2022) 054 [arXiv:2204.08931] [INSPIRE].
G.L. Pimentel and D.-G. Wang, Boostless Cosmological Collider Bootstrap, arXiv:2205.00013 [INSPIRE].
S. Jazayeri and S. Renaux-Petel, Cosmological Bootstrap in Slow Motion, arXiv:2205.10340 [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Holography for inflation using conformal perturbation theory, JHEP 04 (2013) 047 [arXiv:1211.4550] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Holographic predictions for cosmological 3-point functions, JHEP 03 (2012) 091 [arXiv:1112.1967] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111 [arXiv:1304.7760] [INSPIRE].
I. Mata, S. Raju and S. Trivedi, CMB from CFT, JHEP 07 (2013) 015 [arXiv:1211.5482] [INSPIRE].
N. Kundu, A. Shukla and S.P. Trivedi, Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation, JHEP 04 (2015) 061 [arXiv:1410.2606] [INSPIRE].
N. Kundu, A. Shukla and S.P. Trivedi, Ward Identities for Scale and Special Conformal Transformations in Inflation, JHEP 01 (2016) 046 [arXiv:1507.06017] [INSPIRE].
A. Ghosh, N. Kundu, S. Raju and S.P. Trivedi, Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation, JHEP 07 (2014) 011 [arXiv:1401.1426] [INSPIRE].
T. Heckelbacher, I. Sachs, E. Skvortsov and P. Vanhove, Analytical evaluation of cosmological correlation functions, JHEP 08 (2022) 139 [arXiv:2204.07217] [INSPIRE].
P. Benincasa, A.J. McLeod and C. Vergu, Steinmann Relations and the Wavefunction of the Universe, Phys. Rev. D 102 (2020) 125004 [arXiv:2009.03047] [INSPIRE].
Z. Qin and Z.-Z. Xianyu, Helical Inflation Correlators: Partial Mellin-Barnes and Bootstrap Equations, arXiv:2208.13790 [INSPIRE].
S. Akama, S. Hirano and T. Kobayashi, Primordial tensor non-Gaussianities from general single-field inflation with non-Bunch-Davies initial states, Phys. Rev. D 102 (2020) 023513 [arXiv:2003.10686] [INSPIRE].
E. Gourgoulhon, 3+1 formalism and bases of numerical relativity, gr-qc/0703035 [INSPIRE].
S. Jain, R.R. John, A. Mehta, A.A. Nizami and A. Suresh, Higher spin 3-point functions in 3d CFT using spinor-helicity variables, JHEP 09 (2021) 041 [arXiv:2106.00016] [INSPIRE].
S. Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators, Phys. Rev. D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
T. Grall, S. Jazayeri and D. Stefanyszyn, The cosmological phonon: symmetries and amplitudes on sub-horizon scales, JHEP 11 (2020) 097 [arXiv:2005.12937] [INSPIRE].
D. Green, Y. Huang and C.-H. Shen, Inflationary Adler Conditions, arXiv:2208.14544 [INSPIRE].
H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv:0812.1594] [INSPIRE].
D. Anninos, T. Anous, D.Z. Freedman and G. Konstantinidis, Late-time Structure of the Bunch-Davies de Sitter Wavefunction, JCAP 11 (2015) 048 [arXiv:1406.5490] [INSPIRE].
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Cabass, G., Stefanyszyn, D., Supeł, J. et al. On graviton non-Gaussianities in the Effective Field Theory of Inflation. J. High Energ. Phys. 2022, 154 (2022). https://doi.org/10.1007/JHEP10(2022)154
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DOI: https://doi.org/10.1007/JHEP10(2022)154