Built on

C. Sleight and M. Taronna, “Bootstrapping Inflationary Correlators in Mellin Space,” JHEP 02
Original
1907
Earlier work this paper cites.
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, “The cosmological bootstrap: weight-shifting operators and scalar seeds,” JHEP 12
Original
1910
Earlier work this paper cites.
A. E. Lipstein and P. McFadden, “Double copy structure and the flat space limit of conformal correlators in even dimensions,” Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
P. Griffiths, J. Harris, “Principles of algebraic geometry," John Wiley & \& Sons, New York U.S.A, 1978
1978
Earlier work this paper cites.
A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23
1981
Earlier work this paper cites.
V. F. Mukhanov and G. V. Chibisov, “Quantum Fluctuations and a Nonsingular Universe,” JETP Lett. 33
1981
Earlier work this paper cites.
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
Earlier work this paper cites.
A. Albrecht and P. J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
J. B. Hartle and S. W. Hawking, “Wave Function of the Universe,” Phys. Rev. D 28
1983
Earlier work this paper cites.
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
Earlier work this paper cites.
H. Liu and A. A. Tseytlin, “On four point functions in the CFT / AdS correspondence,” Phys. Rev. D 59
1999
Earlier work this paper cites.
A. Strominger, “Inflation and the dS / CFT correspondence,” JHEP 11
2001
Earlier work this paper cites.
J. M. Maldacena, “Non-Gaussian features of primordial fluctuations in single field inflationary models,” JHEP 05
2003
Earlier work this paper cites.
D. Green and E. Pajer, “On the Symmetries of Cosmological Perturbations,” JCAP 09
Original
2004
Earlier work this paper cites.
S. Weinberg, “Quantum contributions to cosmological correlations,” Phys. Rev. D 72
2005
Earlier work this paper cites.
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
Earlier work this paper cites.
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, “The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization,” [arXiv:2005.04234 [hep-th]]
Original
2005
Earlier work this paper cites.
C. Sleight and M. Taronna, “From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing,” [arXiv:2007.09993 [hep-th]]
Original
2007
Earlier work this paper cites.
L. Eberhardt, S. Komatsu and S. Mizera, “Scattering equations in AdS: scalar correlators in arbitrary dimensions,” JHEP 11
Original
2007
Earlier work this paper cites.
K. Roehrig and D. Skinner, “Ambitwistor Strings and the Scattering Equations on AdS 3 × {}_{3}\times S 3 ,” [arXiv:2007.07234 [hep-th]]
Original
2007
Earlier work this paper cites.
J. A. Farrow, Y. Geyer, A. E. Lipstein, R. Monteiro and R. Stark-Muchão, “Propagators, BCFW recursion and new scattering equations at one loop,” JHEP 10
Original
2007
Earlier work this paper cites.

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2021

Cosmological Scattering Equations

Gomez, Humberto, Jusinskas, Renann Lipinski, Lipstein, Arthur

Understand

We propose a worldsheet formula for tree-level correlation functions describing a scalar field with arbitrary mass and quartic self-interaction in de Sitter space, which is a simple model for inflationary cosmology.

The correlation functions are located on the future boundary of the spacetime and are Fourier-transformed to momentum space.
Our formula is supported on mass-deformed scattering equations involving conformal generators in momentum space and reduces to the CHY formula for $\phi^4$ amplitudes in the flat space limit.
Using the global residue theorem, we verify that it reproduces the Witten diagram expansion at four and six points, and sketch the extension to $n$ points.

Built on

C. Sleight and M. Taronna, “Bootstrapping Inflationary Correlators in Mellin Space,” JHEP 02
Original
1907
Earlier work this paper cites.
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, “The cosmological bootstrap: weight-shifting operators and scalar seeds,” JHEP 12
Original
1910
Earlier work this paper cites.
A. E. Lipstein and P. McFadden, “Double copy structure and the flat space limit of conformal correlators in even dimensions,” Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
P. Griffiths, J. Harris, “Principles of algebraic geometry," John Wiley & \& Sons, New York U.S.A, 1978
1978
Earlier work this paper cites.
A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23
1981
Earlier work this paper cites.
V. F. Mukhanov and G. V. Chibisov, “Quantum Fluctuations and a Nonsingular Universe,” JETP Lett. 33
1981
Earlier work this paper cites.
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
Earlier work this paper cites.
A. Albrecht and P. J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett. 48
1982
Earlier work this paper cites.
J. B. Hartle and S. W. Hawking, “Wave Function of the Universe,” Phys. Rev. D 28
1983
Earlier work this paper cites.
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
Earlier work this paper cites.
H. Liu and A. A. Tseytlin, “On four point functions in the CFT / AdS correspondence,” Phys. Rev. D 59
1999
Earlier work this paper cites.
A. Strominger, “Inflation and the dS / CFT correspondence,” JHEP 11
2001
Earlier work this paper cites.
J. M. Maldacena, “Non-Gaussian features of primordial fluctuations in single field inflationary models,” JHEP 05
2003
Earlier work this paper cites.
D. Green and E. Pajer, “On the Symmetries of Cosmological Perturbations,” JCAP 09
Original
2004
Earlier work this paper cites.
S. Weinberg, “Quantum contributions to cosmological correlations,” Phys. Rev. D 72
2005
Earlier work this paper cites.
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
Earlier work this paper cites.
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, “The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization,” [arXiv:2005.04234 [hep-th]]
Original
2005
Earlier work this paper cites.
C. Sleight and M. Taronna, “From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing,” [arXiv:2007.09993 [hep-th]]
Original
2007
Earlier work this paper cites.
L. Eberhardt, S. Komatsu and S. Mizera, “Scattering equations in AdS: scalar correlators in arbitrary dimensions,” JHEP 11
Original
2007
Earlier work this paper cites.
K. Roehrig and D. Skinner, “Ambitwistor Strings and the Scattering Equations on AdS 3 × {}_{3}\times S 3 ,” [arXiv:2007.07234 [hep-th]]
Original
2007
Earlier work this paper cites.
J. A. Farrow, Y. Geyer, A. E. Lipstein, R. Monteiro and R. Stark-Muchão, “Propagators, BCFW recursion and new scattering equations at one loop,” JHEP 10
Original
2007
Earlier work this paper cites.