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The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds · Around

2019

The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds

Baumann, Daniel, Pueyo, Carlos Duaso, Joyce, Austin et al.

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A key insight of the bootstrap approach to cosmological correlations is the fact that all correlators of slow-roll inflation can be reduced to a unique building block---the four-point function of conformally coupled scalars, arising from the exchange of a massive scalar.

Correlators corresponding to the exchange of particles with spin are then obtained by applying a spin-raising operator to the scalar-exchange solution.
Similarly, the correlators of massless external fields can be derived by acting with a suitable weight-raising operator.
In this paper, we present a systematic and highly streamlined derivation of these operators (and their generalizations) using tools of conformal field theory.

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C. Corianò and M. Maglio, “On Some Hypergeometric Solutions of the Conformal Ward Identities of Scalar Four-Point Functions in Momentum Space,” JHEP
Original
1903
Earlier work this paper cites.
H. Isono, T. Noumi, and T. Takeuchi, “Momentum Space Conformal Three-Point Functions of Conserved Currents and a General Spinning Operator,” JHEP
Original
1903
Earlier work this paper cites.
S. Albayrak, C. Chowdhury, and S. Kharel, “New Relation for AdS Amplitudes,” arXiv:1904.10043 [hep-th]
Original
1904
Earlier work this paper cites.
E. Joung, K. Mkrtchyan, and G. Poghosyan, “Looking for Partially Massless Gravity,” JHEP
Original
1904
Earlier work this paper cites.
C. Sleight, “A Mellin Space Approach to Cosmological Correlators,” arXiv:1906.12302 [hep-th]
Original
1906
Earlier work this paper cites.
S. Kim, T. Noumi, K. Takeuchi, and S. Zhou, “Heavy Spinning Particles from Signs of Primordial Non-Gaussianities: Beyond the Positivity Bounds,” arXiv:1906.11840 [hep-th]
Original
1906
Earlier work this paper cites.
N. Boulanger, C. Deffayet, S. Garcia-Saenz, and L. Traina, “A Theory for Multiple Partially Massless Spin-2 Fields,” arXiv:1906.03868 [hep-th]
Original
1906
Earlier work this paper cites.
C. Sleight and M. Taronna, “Bootstrapping Inflationary Correlators in Mellin Space,” arXiv:1907.01143 [hep-th]
Original
1907
Earlier work this paper cites.
S. Alexander, S. J. Gates, L. Jenks, K. Koutrolikos, and E. McDonough, “Higher-Spin Supersymmetry at the Cosmological Collider: Sculpting SUSY Rilles in the CMB,” arXiv:1907.05829 [hep-th]
Original
1907
Earlier work this paper cites.
R. Erramilli, L. Iliesiu, and P. Kravchuk, “Recursion Relation for General 3d Blocks,” arXiv:1907.11247 [hep-th]
Original
1907
Earlier work this paper cites.
H. Isono, T. Noumi, and G. Shiu, “Momentum Space Approach to Crossing Symmetric CFT Correlators II: General Spacetime Dimension,” arXiv:1908.04572 [hep-th]
Original
1908
Earlier work this paper cites.
S. Albayrak and S. Kharel, “Towards the Higher-Point Holographic Momentum Space Amplitudes II: Gravitons,” arXiv:1908.01835 [hep-th]
Original
1908
Earlier work this paper cites.
S. Kumar and R. Sundrum, “Cosmological Collider Physics and the Curvaton,” arXiv:1908.11378 [hep-ph]
Original
1908
Earlier work this paper cites.
T. Bautista and H. Godazgar, “Lorentzian CFT Three-Point Functions in Momentum Space,” arXiv:1908.04733 [hep-th]
Original
1908
Earlier work this paper cites.
P. Benincasa, “Cosmological Polytopes and the Wavefuncton of the Universe for Light States,” arXiv:1909.02517 [hep-th]
Original
1909
Earlier work this paper cites.
T. Liu, X. Tong, Y. Wang, and Z.-Z. Xianyu, “Probing P and CP Violations on the Cosmological Collider,” arXiv:1909.01819 [hep-ph]
Original
1909
Earlier work this paper cites.
M. Gillioz, “Conformal Three-Point Functions and the Lorentzian OPE in Momentum Space,” arXiv:1909.00878 [hep-th]
Original
1909
Earlier work this paper cites.
A. Bzowski, P. McFadden, and K. Skenderis, “Conformal Four-Point Functions in Momentum Space,” arXiv:1910.10162 [hep-th]
Original
1910
Earlier work this paper cites.
P. A. M. Dirac, “Wave Equations in Conformal Space,” Annals Math
1936
Earlier work this paper cites.
A. Polyakov, “Conformal Symmetry of Critical Fluctuations,” JETP Lett
1970
Earlier work this paper cites.
V. Dobrev, G. Mack, V. Petkova, S. Petrova, and I. Todorov, “Harmonic Analysis on the n n -Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory,” Lect. Notes Phys
1977
Earlier work this paper cites.
S. Deser and R. Nepomechie, “Gauge Invariance Versus Masslessness in De Sitter Space,” Annals Phys
1984
Earlier work this paper cites.
L. Brink, R. Metsaev, and M. Vasiliev, “How Massless are Massless Fields in AdS(d),” Nucl. Phys
2000
Earlier work this paper cites.
S. Deser and A. Waldron, “Partial Masslessness of Higher Spins in (A)dS,” Nucl. Phys
2001
Earlier work this paper cites.
L. Dolan, C. R. Nappi, and E. Witten, “Conformal operators for partially massless states,” JHEP
2001
Earlier work this paper cites.
P. Creminelli, “On Non-Gaussianities in Single-Field Inflation,” JCAP
2003
Earlier work this paper cites.

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