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A de Sitter S-matrix from amputated cosmological correlators

Published 8 Apr 2024 in hep-th and gr-qc | (2404.05712v1)

Abstract: Extending scattering to states with unphysical mass values (particles off their mass shell'') has been instrumental in developing modern amplitude technology for Minkowski spacetime. Here, we study the off-shell correlators which underpin the recently proposed S-matrix for scattering on de Sitter spacetime. By labelling each particle with both a spatial momentum and an independentenergy'' variable (the de Sitter analogue of a 4-momentum), we find that the practical computation of these correlators is greatly simplified. This allows us to derive compact expressions for all 3- and 4-particle S-matrices at tree-level for scalar fields coupled through any derivative interactions. As on Minkowski, we find that the 3-particle and exchange part of the 4-particle S-matrices are unique (up to crossing). The remaining contact part of the 4-particle S-matrix is an analytic function of just two differential operators, which become the usual Mandelstam variables in the Minkowski limit. Finally, we introduce a spectral decomposition for the tree-level exchange of a heavy field responsible for a cosmological collider signal. Once projected onto physical mass eigenstates, these S-matrix elements encode the statistical properties of the early inflationary perturbations.

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References (108)
  1. G. F. Chew, S𝑆Sitalic_S-matrix theory of strong interactions. Benjamin, New York, 1961.
  2. Cambridge Univ. Press, Cambridge, 1966.
  3. Springer Berlin Heidelberg, 1969.
  4. R. E. Cutkosky, “Singularities and discontinuities of Feynman amplitudes,” J. Math. Phys. 1 (1960) 429–433.
  5. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “One loop n point gauge theory amplitudes, unitarity and collinear limits,” Nucl. Phys. B 425 (1994) 217–260, arXiv:hep-ph/9403226.
  6. Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing gauge theory tree amplitudes into loop amplitudes,” Nucl. Phys. B 435 (1995) 59–101, arXiv:hep-ph/9409265.
  7. H. Elvang and Y.-t. Huang, “Scattering Amplitudes,” arXiv:1308.1697 [hep-th].
  8. Z. Bern and J. Trnka, “Snowmass TF04 Report: Scattering Amplitudes and their Applications,” arXiv:2210.03146 [hep-th].
  9. A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng, “Snowmass White Paper: Gravitational Waves and Scattering Amplitudes,” in Snowmass 2021. 4, 2022. arXiv:2204.05194 [hep-th].
  10. A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,” JHEP 10 (2006) 014, arXiv:hep-th/0602178.
  11. A. V. Manohar and V. Mateu, “Dispersion Relation Bounds for pi pi Scattering,” Phys. Rev. D 77 (2008) 094019, arXiv:0801.3222 [hep-ph].
  12. Z. Komargodski and A. Schwimmer, “On Renormalization Group Flows in Four Dimensions,” JHEP 12 (2011) 099, arXiv:1107.3987 [hep-th].
  13. M. A. Luty, J. Polchinski, and R. Rattazzi, “The a𝑎aitalic_a-theorem and the Asymptotics of 4D Quantum Field Theory,” JHEP 01 (2013) 152, arXiv:1204.5221 [hep-th].
  14. M. Kruczenski, J. Penedones, and B. C. van Rees, “Snowmass White Paper: S-matrix Bootstrap,” arXiv:2203.02421 [hep-th].
  15. C. de Rham, S. Kundu, M. Reece, A. J. Tolley, and S.-Y. Zhou, “Snowmass White Paper: UV Constraints on IR Physics,” in Snowmass 2021. 3, 2022. arXiv:2203.06805 [hep-th].
  16. X. Chen and Y. Wang, “Quasi-Single Field Inflation and Non-Gaussianities,” JCAP 04 (2010) 027, arXiv:0911.3380 [hep-th].
  17. N. Arkani-Hamed and J. Maldacena, “Cosmological Collider Physics,” arXiv:1503.08043 [hep-th].
  18. G. Cabass, O. H. E. Philcox, M. M. Ivanov, K. Akitsu, S.-F. Chen, M. Simonović, and M. Zaldarriaga, “BOSS Constraints on Massive Particles during Inflation: The Cosmological Collider in Action,” arXiv:2404.01894 [astro-ph.CO].
  19. D. Baumann, D. Green, A. Joyce, E. Pajer, G. L. Pimentel, C. Sleight, and M. Taronna, “Snowmass White Paper: The Cosmological Bootstrap,” in Snowmass 2021. 3, 2022. arXiv:2203.08121 [hep-th].
  20. P. Benincasa, “Amplitudes meet Cosmology: A (Scalar) Primer,” arXiv:2203.15330 [hep-th].
  21. J. Bonifacio, E. Pajer, and D.-G. Wang, “From amplitudes to contact cosmological correlators,” JHEP 10 (2021) 001, arXiv:2106.15468 [hep-th].
  22. M. H. G. Lee, “From amplitudes to analytic wavefunctions,” JHEP 03 (2024) 058, arXiv:2310.01525 [hep-th].
  23. C. Chowdhury, A. Lipstein, J. Mei, I. Sachs, and P. Vanhove, “The Subtle Simplicity of Cosmological Correlators,” arXiv:2312.13803 [hep-th].
  24. H. Goodhew, S. Jazayeri, and E. Pajer, “The Cosmological Optical Theorem,” JCAP 04 (2021) 021, arXiv:2009.02898 [hep-th].
  25. S. Céspedes, A.-C. Davis, and S. Melville, “On the time evolution of cosmological correlators,” JHEP 02 (2021) 012, arXiv:2009.07874 [hep-th].
  26. S. Melville and E. Pajer, “Cosmological Cutting Rules,” JHEP 05 (2021) 249, arXiv:2103.09832 [hep-th].
  27. H. Goodhew, S. Jazayeri, M. H. Gordon Lee, and E. Pajer, “Cutting cosmological correlators,” JCAP 08 (2021) 003, arXiv:2104.06587 [hep-th].
  28. 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 [hep-th].
  29. S. Jazayeri, E. Pajer, and D. Stefanyszyn, “From locality and unitarity to cosmological correlators,” JHEP 10 (2021) 065, arXiv:2103.08649 [hep-th].
  30. S. Albayrak, P. Benincasa, and C. D. Pueyo, “Perturbative Unitarity and the Wavefunction of the Universe,” arXiv:2305.19686 [hep-th].
  31. S. Agui-Salcedo and S. Melville, “The cosmological tree theorem,” JHEP 12 (2023) 076, arXiv:2308.00680 [hep-th].
  32. S. A. Salcedo, M. H. G. Lee, S. Melville, and E. Pajer, “The Analytic Wavefunction,” JHEP 06 (2023) 020, arXiv:2212.08009 [hep-th].
  33. C. Armstrong, H. Goodhew, A. Lipstein, and J. Mei, “Graviton trispectrum from gluons,” JHEP 08 (2023) 206, arXiv:2304.07206 [hep-th].
  34. H. Lee and X. Wang, “Cosmological double-copy relations,” Phys. Rev. D 108 (2023) no. 6, L061702, arXiv:2212.11282 [hep-th].
  35. S. Melville and G. L. Pimentel, “A de Sitter S𝑆Sitalic_S-matrix for the masses,” arXiv:2309.07092 [hep-th].
  36. 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 [hep-th].
  37. 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 [hep-th].
  38. 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 [hep-th].
  39. A. Bzowski, P. McFadden, and K. Skenderis, “Implications of conformal invariance in momentum space,” JHEP 03 (2014) 111, arXiv:1304.7760 [hep-th].
  40. A. Bzowski, P. McFadden, and K. Skenderis, “Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies,” JHEP 03 (2016) 066, arXiv:1510.08442 [hep-th].
  41. D. Baumann, Cosmology. Cambridge University Press, 7, 2022.
  42. H. Gomez, R. L. Jusinskas, and A. Lipstein, “Cosmological Scattering Equations,” Phys. Rev. Lett. 127 (2021) no. 25, 251604, arXiv:2106.11903 [hep-th].
  43. H. Gomez, R. Lipinski Jusinskas, and A. Lipstein, “Cosmological scattering equations at tree-level and one-loop,” JHEP 07 (2022) 004, arXiv:2112.12695 [hep-th].
  44. 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 [hep-th].
  45. F. A. Berends and W. T. Giele, “Recursive Calculations for Processes with n Gluons,” Nucl. Phys. B 306 (1988) 759–808.
  46. D. S. Jones, “The kontorovich-lebedev transform,” IMA Journal of Applied Mathematics 26 (1980) no. 2, 133–141.
  47. Y. Gutiérrez-Tovar and J. Méndez-Pérez, “The kontorovich–lebedev integral transformation with a hankel function kernel in a space of generalized functions of doubly exponential descent,” Journal of Mathematical Analysis and Applications 328 (2007) no. 1, 359–369. https://www.sciencedirect.com/science/article/pii/S0022247X0600518X.
  48. D. Karateev, P. Kravchuk, and D. Simmons-Duffin, “Harmonic Analysis and Mean Field Theory,” JHEP 10 (2019) 217, arXiv:1809.05111 [hep-th].
  49. B. Allen, “Vacuum States in de Sitter Space,” Phys. Rev. D 32 (1985) 3136.
  50. D. Green, Y. Huang, C.-H. Shen, and D. Baumann, “Positivity from Cosmological Correlators,” arXiv:2310.02490 [hep-th].
  51. M. Hogervorst, J. a. Penedones, and K. S. Vaziri, “Towards the non-perturbative cosmological bootstrap,” JHEP 02 (2023) 162, arXiv:2107.13871 [hep-th].
  52. J. Penedones, K. Salehi Vaziri, and Z. Sun, “Hilbert space of Quantum Field Theory in de Sitter spacetime,” arXiv:2301.04146 [hep-th].
  53. M. Loparco, J. Penedones, K. Salehi Vaziri, and Z. Sun, “The Källén-Lehmann representation in de Sitter spacetime,” JHEP 12 (2023) 159, arXiv:2306.00090 [hep-th].
  54. M. H. G. Lee, C. McCulloch, and E. Pajer, “Leading loops in cosmological correlators,” JHEP 11 (2023) 038, arXiv:2305.11228 [hep-th].
  55. Z.-Z. Xianyu and H. Zhang, “Bootstrapping one-loop inflation correlators with the spectral decomposition,” JHEP 04 (2023) 103, arXiv:2211.03810 [hep-th].
  56. Z. Qin and Z.-Z. Xianyu, “Nonanalyticity and on-shell factorization of inflation correlators at all loop orders,” JHEP 01 (2024) 168, arXiv:2308.14802 [hep-th].
  57. Z. Qin and Z.-Z. Xianyu, “Inflation correlators at the one-loop order: nonanalyticity, factorization, cutting rule, and OPE,” JHEP 09 (2023) 116, arXiv:2304.13295 [hep-th].
  58. A. Bzowski, P. McFadden, and K. Skenderis, “Renormalisation of IR divergences and holography in de Sitter,” arXiv:2312.17316 [hep-th].
  59. K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19 (2002) 5849–5876, arXiv:hep-th/0209067.
  60. D.-G. Wang, G. L. Pimentel, and A. Achúcarro, “Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisited,” JCAP 05 (2023) 043, arXiv:2212.14035 [astro-ph.CO].
  61. V. Gorbenko and L. Senatore, “λ⁢ϕ4𝜆superscriptitalic-ϕ4\lambda\phi^{4}italic_λ italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT in dS,” arXiv:1911.00022 [hep-th].
  62. M. Baumgart and R. Sundrum, “De Sitter Diagrammar and the Resummation of Time,” JHEP 07 (2020) 119, arXiv:1912.09502 [hep-th].
  63. D. Green and A. Premkumar, “Dynamical RG and Critical Phenomena in de Sitter Space,” JHEP 04 (2020) 064, arXiv:2001.05974 [hep-th].
  64. T. Cohen and D. Green, “Soft de Sitter Effective Theory,” JHEP 12 (2020) 041, arXiv:2007.03693 [hep-th].
  65. S. Céspedes, A.-C. Davis, and D.-G. Wang, “On the IR Divergences in de Sitter Space: loops, resummation and the semi-classical wavefunction,” arXiv:2311.17990 [hep-th].
  66. 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 [hep-th].
  67. G. Cabass, E. Pajer, D. Stefanyszyn, and J. Supel, “Bootstrapping large graviton non-Gaussianities,” JHEP 05 (2022) 077, arXiv:2109.10189 [hep-th].
  68. J. Bonifacio, H. Goodhew, A. Joyce, E. Pajer, and D. Stefanyszyn, “The graviton four-point function in de Sitter space,” JHEP 06 (2023) 212, arXiv:2212.07370 [hep-th].
  69. A. Bzowski, P. McFadden, and K. Skenderis, “A handbook of holographic 4-point functions,” JHEP 12 (2022) 039, arXiv:2207.02872 [hep-th].
  70. F. Caloro and P. McFadden, “𝒜𝒜\mathcal{A}caligraphic_A-hypergeometric functions and creation operators for Feynman and Witten diagrams,” arXiv:2309.15895 [hep-th].
  71. Z. Qin and Z.-Z. Xianyu, “Helical inflation correlators: partial Mellin-Barnes and bootstrap equations,” JHEP 04 (2023) 059, arXiv:2208.13790 [hep-th].
  72. Z. Qin and Z.-Z. Xianyu, “Closed-form formulae for inflation correlators,” JHEP 07 (2023) 001, arXiv:2301.07047 [hep-th].
  73. Z.-Z. Xianyu and J. Zang, “Inflation correlators with multiple massive exchanges,” JHEP 03 (2024) 070, arXiv:2309.10849 [hep-th].
  74. B. Fan and Z.-Z. Xianyu, “Cosmological Amplitudes in Power-Law FRW Universe,” arXiv:2403.07050 [hep-th].
  75. A. Bzowski, P. McFadden, and K. Skenderis, “Conformal n𝑛nitalic_n-point functions in momentum space,” Phys. Rev. Lett. 124 (2020) no. 13, 131602, arXiv:1910.10162 [hep-th].
  76. A. Bzowski, P. McFadden, and K. Skenderis, “Conformal correlators as simplex integrals in momentum space,” JHEP 01 (2021) 192, arXiv:2008.07543 [hep-th].
  77. F. Caloro and P. McFadden, “Shift operators from the simplex representation in momentum-space CFT,” JHEP 03 (2023) 106, arXiv:2212.03887 [hep-th].
  78. N. Arkani-Hamed, D. Baumann, A. Hillman, A. Joyce, H. Lee, and G. L. Pimentel, “Kinematic Flow and the Emergence of Time,” arXiv:2312.05300 [hep-th].
  79. N. Arkani-Hamed, D. Baumann, A. Hillman, A. Joyce, H. Lee, and G. L. Pimentel, “Differential Equations for Cosmological Correlators,” arXiv:2312.05303 [hep-th].
  80. D. Green and E. Pajer, “On the Symmetries of Cosmological Perturbations,” JCAP 09 (2020) 032, arXiv:2004.09587 [hep-th].
  81. E. Pajer, D. Stefanyszyn, and J. Supel, “The Boostless Bootstrap: Amplitudes without Lorentz boosts,” JHEP 12 (2020) 198, arXiv:2007.00027 [hep-th]. [Erratum: JHEP 04, 023 (2022)].
  82. E. Pajer, “Building a Boostless Bootstrap for the Bispectrum,” JCAP 01 (2021) 023, arXiv:2010.12818 [hep-th].
  83. C. Duaso Pueyo and E. Pajer, “A cosmological bootstrap for resonant non-Gaussianity,” JHEP 24 (2020) 098, arXiv:2311.01395 [hep-th].
  84. G. L. Pimentel and D.-G. Wang, “Boostless cosmological collider bootstrap,” JHEP 10 (2022) 177, arXiv:2205.00013 [hep-th].
  85. Z. Du and D. Stefanyszyn, “Soft Theorems for Boostless Amplitudes,” arXiv:2403.05459 [hep-th].
  86. J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 03 (2011) 025, arXiv:1011.1485 [hep-th].
  87. A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, “A Natural Language for AdS/CFT Correlators,” JHEP 11 (2011) 095, arXiv:1107.1499 [hep-th].
  88. S. Raju, “New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators,” Phys. Rev. D 85 (2012) 126009, arXiv:1201.6449 [hep-th].
  89. J. Penedones, J. A. Silva, and A. Zhiboedov, “Nonperturbative Mellin Amplitudes: Existence, Properties, Applications,” JHEP 08 (2020) 031, arXiv:1912.11100 [hep-th].
  90. C. Sleight, “A Mellin Space Approach to Cosmological Correlators,” JHEP 01 (2020) 090, arXiv:1906.12302 [hep-th].
  91. C. Sleight and M. Taronna, “Bootstrapping Inflationary Correlators in Mellin Space,” JHEP 02 (2020) 098, arXiv:1907.01143 [hep-th].
  92. C. Sleight and M. Taronna, “From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing,” Phys. Rev. D 104 (2021) no. 8, L081902, arXiv:2007.09993 [hep-th].
  93. C. Sleight and M. Taronna, “From dS to AdS and back,” JHEP 12 (2021) 074, arXiv:2109.02725 [hep-th].
  94. L. Di Pietro, V. Gorbenko, and S. Komatsu, “Analyticity and unitarity for cosmological correlators,” JHEP 03 (2022) 023, arXiv:2108.01695 [hep-th].
  95. L. Di Pietro, V. Gorbenko, and S. Komatsu, “Cosmological Correlators at Finite Coupling,” arXiv:2312.17195 [hep-th].
  96. D. Marolf, I. A. Morrison, and M. Srednicki, “Perturbative S-matrix for massive scalar fields in global de Sitter space,” Class. Quant. Grav. 30 (2013) 155023, arXiv:1209.6039 [hep-th].
  97. D. Baumann and D. Green, “Equilateral Non-Gaussianity and New Physics on the Horizon,” JCAP 09 (2011) 014, arXiv:1102.5343 [hep-th].
  98. D. Baumann, D. Green, H. Lee, and R. A. Porto, “Signs of Analyticity in Single-Field Inflation,” Phys. Rev. D 93 (2016) no. 2, 023523, arXiv:1502.07304 [hep-th].
  99. T. Grall and S. Melville, “Inflation in motion: unitarity constraints in effective field theories with (spontaneously) broken Lorentz symmetry,” JCAP 09 (2020) 017, arXiv:2005.02366 [gr-qc].
  100. T. Grall and S. Melville, “Positivity bounds without boosts: New constraints on low energy effective field theories from the UV,” Phys. Rev. D 105 (2022) no. 12, L121301, arXiv:2102.05683 [hep-th].
  101. D. Green, Y. Huang, and C.-H. Shen, “Inflationary Adler conditions,” Phys. Rev. D 107 (2023) no. 4, 043534, arXiv:2208.14544 [hep-th].
  102. M. Freytsis, S. Kumar, G. N. Remmen, and N. L. Rodd, “Multifield positivity bounds for inflation,” JHEP 09 (2023) 041, arXiv:2210.10791 [hep-th].
  103. S. Melville and J. Noller, “Positivity in the Sky: Constraining dark energy and modified gravity from the UV,” Phys. Rev. D 101 (2020) no. 2, 021502, arXiv:1904.05874 [astro-ph.CO]. [Erratum: Phys.Rev.D 102, 049902 (2020)].
  104. C. de Rham, S. Melville, and J. Noller, “Positivity bounds on dark energy: when matter matters,” JCAP 08 (2021) 018, arXiv:2103.06855 [astro-ph.CO].
  105. A.-C. Davis and S. Melville, “Scalar fields near compact objects: resummation versus UV completion,” JCAP 11 (2021) 012, arXiv:2107.00010 [gr-qc].
  106. S. Melville and J. Noller, “Positivity bounds from multiple vacua and their cosmological consequences,” JCAP 06 (2022) no. 06, 031, arXiv:2202.01222 [hep-th].
  107. D. de Boe, G. Ye, F. Renzi, I. S. Albuquerque, N. Frusciante, and A. Silvestri, “Phenomenology of Horndeski Gravity under Positivity Bounds,” arXiv:2403.13096 [astro-ph.CO].
  108. The University Press, 1922.
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