Abstract
We study the fundamentals of quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. This finding simplifies dramatically perturbative computations, as well as allows us to establish basic properties of these correlators, which comprise a Euclidean CFT. We use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. This statement does not rely on the use of Euclidean AdS Lagrangians and holds non-perturbatively. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one- loop-resummed exchange diagrams. An exchanged particle appears as a resonant feature in the spectral density which can be potentially useful in experimental searches.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
C. Sleight and M. Taronna, From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing, arXiv:2007.09993 [INSPIRE].
V. Gorbenko and L. Senatore, λϕ4 in dS, arXiv:1911.00022 [INSPIRE].
J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [INSPIRE].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].
T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [INSPIRE].
N. Turok, B. Craps and T. Hertog, From big crunch to big bang with AdS/CFT, arXiv:0711.1824 [INSPIRE].
B. Craps, T. Hertog and N. Turok, On the Quantum Resolution of Cosmological Singularities using AdS/CFT, Phys. Rev. D 86 (2012) 043513 [arXiv:0712.4180] [INSPIRE].
J.L.F. Barbón and E. Rabinovici, AdS Crunches, CFT Falls And Cosmological Complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].
J.L.F. Barbón and E. Rabinovici, Conformal Complementarity Maps, JHEP 12 (2013) 023 [arXiv:1308.1921] [INSPIRE].
S.P. Kumar and V. Vaganov, Probing crunching AdS cosmologies, JHEP 02 (2016) 026 [arXiv:1510.03281] [INSPIRE].
M. Hogervorst, J. Penedones and K.S. Vaziri, Towards the non-perturbative cosmological bootstrap, arXiv:2107.13871 [INSPIRE].
M. Spradlin, A. Strominger and A. Volovich, Les Houches lectures on de Sitter space, in Les Houches Summer School: Session 76: Euro Summer School on Unity of Fundamental Physics: Gravity, Gauge Theory and Strings, Les Houches France (2001), pg. 423 [hep-th/0110007] [INSPIRE].
D. Anninos, de Sitter Musings, Int. J. Mod. Phys. A 27 (2012) 1230013 [arXiv:1205.3855] [INSPIRE].
T. Newton, A note on the representations of the de Sitter group, Ann. Math. 51 (1950) 730.
L. Thomas, On unitary representations of the group of de sitter space, Ann. Math. 42 (1941) 113.
V.K. Dobrev, G. Mack, I.T. Todorov, V.B. Petkova and S.G. Petrova, On the Clebsch-Gordan Expansion for the Lorentz Group in n Dimensions, Rept. Math. Phys. 9 (1976) 219 [INSPIRE].
V. Dobrev et al., Harmonic analysis on the n-dimensional Lorentz group and its application to conformal quantum field theory, Lect. Notes Phys. 63 (1977) 1.
D. Baumann, G. Goon, H. Lee and G.L. Pimentel, Partially Massless Fields During Inflation, JHEP 04 (2018) 140 [arXiv:1712.06624] [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, in Strings 2001: International Conference, Mumbai India (2001) [hep-th/0106109] [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
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] [INSPIRE].
J. Cotler and K. Jensen, Emergent unitarity in de Sitter from matrix integrals, JHEP 12 (2021) 089 [arXiv:1911.12358] [INSPIRE].
E. Albrychiewicz and Y. Neiman, Scattering in the static patch of de Sitter space, Phys. Rev. D 103 (2021) 065014 [arXiv:2012.13584] [INSPIRE].
N. Arkani-Hamed, P. Benincasa and A. Postnikov, Cosmological Polytopes and the Wavefunction of the Universe, arXiv:1709.02813 [INSPIRE].
A. Hillman, Symbol Recursion for the dS Wave Function, arXiv:1912.09450 [INSPIRE].
P. Benincasa, Cosmological Polytopes and the Wavefuncton of the Universe for Light States, arXiv:1909.02517 [INSPIRE].
D. Meltzer, The inflationary wavefunction from analyticity and factorization, JCAP 12 (2021) 018 [arXiv:2107.10266] [INSPIRE].
E. Pajer, D. Stefanyszyn and J. Supel, The Boostless Bootstrap: Amplitudes without Lorentz boosts, JHEP 12 (2020) 198 [arXiv:2007.00027] [INSPIRE].
S. Céspedes, A.-C. Davis and S. Melville, On the time evolution of cosmological correlators, JHEP 02 (2021) 012 [arXiv:2009.07874] [INSPIRE].
H. Goodhew, S. Jazayeri, M.H. Gordon Lee and E. Pajer, Cutting cosmological correlators, JCAP 08 (2021) 003 [arXiv:2104.06587] [INSPIRE].
H. Goodhew, S. Jazayeri and E. Pajer, The Cosmological Optical Theorem, JCAP 04 (2021) 021 [arXiv:2009.02898] [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, arXiv:2106.05294 [INSPIRE].
D. Anninos, F. Denef, R. Monten and Z. Sun, Higher Spin de Sitter Hilbert Space, JHEP 10 (2019) 071 [arXiv:1711.10037] [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].
D. Anninos, S.A. Hartnoll and D.M. Hofman, Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline, Class. Quant. Grav. 29 (2012) 075002 [arXiv:1109.4942] [INSPIRE].
H. Isono, H.M. Liu and T. Noumi, Wavefunctions in dS/CFT revisited: principal series and double-trace deformations, JHEP 04 (2021) 166 [arXiv:2011.09479] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
V. Gorbenko, S. Rychkov and B. Zan, Walking, Weak first-order transitions, and Complex CFTs, JHEP 10 (2018) 108 [arXiv:1807.11512] [INSPIRE].
R.G. Leigh and A.C. Petkou, SL(2, ℤ) action on three-dimensional CFTs and holography, JHEP 12 (2003) 020 [hep-th/0309177] [INSPIRE].
G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].
S. Giombi, I.R. Klebanov, S.S. Pufu, B.R. Safdi and G. Tarnopolsky, AdS Description of Induced Higher-Spin Gauge Theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].
J. Cotler, K. Jensen and A. Maloney, Low-dimensional de Sitter quantum gravity, JHEP 06 (2020) 048 [arXiv:1905.03780] [INSPIRE].
A. Goel, L.V. Iliesiu, J. Kruthoff and Z. Yang, Classifying boundary conditions in JT gravity: from energy-branes to α-branes, JHEP 04 (2021) 069 [arXiv:2010.12592] [INSPIRE].
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
D. Seery, One-loop corrections to a scalar field during inflation, JCAP 11 (2007) 025 [arXiv:0707.3377] [INSPIRE].
P. Adshead, R. Easther and E.A. Lim, The ’in-in’ Formalism and Cosmological Perturbations, Phys. Rev. D 80 (2009) 083521 [arXiv:0904.4207] [INSPIRE].
L. Senatore and M. Zaldarriaga, On Loops in Inflation, JHEP 12 (2010) 008 [arXiv:0912.2734] [INSPIRE].
L. Senatore, Lectures on Inflation, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, Boulder U.S.A. (2017), pg. 447 [arXiv:1609.00716] [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].
C. Sleight, A Mellin Space Approach to Cosmological Correlators, JHEP 01 (2020) 090 [arXiv:1906.12302] [INSPIRE].
C. Sleight and M. Taronna, Bootstrapping Inflationary Correlators in Mellin Space, JHEP 02 (2020) 098 [arXiv:1907.01143] [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].
D. Marolf and I.A. Morrison, The IR stability of de Sitter: Loop corrections to scalar propagators, Phys. Rev. D 82 (2010) 105032 [arXiv:1006.0035] [INSPIRE].
D. Marolf and I.A. Morrison, The IR stability of de Sitter QFT: results at all orders, Phys. Rev. D 84 (2011) 044040 [arXiv:1010.5327] [INSPIRE].
D. Marolf and I.A. Morrison, The IR stability of de Sitter QFT: Physical initial conditions, Gen. Rel. Grav. 43 (2011) 3497 [arXiv:1104.4343] [INSPIRE].
D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
I. Mata, S. Raju and S. Trivedi, CMB from CFT, JHEP 07 (2013) 015 [arXiv:1211.5482] [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].
D. Carmi, L. Di Pietro and S. Komatsu, A Study of Quantum Field Theories in AdS at Finite Coupling, JHEP 01 (2019) 200 [arXiv:1810.04185] [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07 (2018) 085 [arXiv:1711.03816] [INSPIRE].
D. Karateev, P. Kravchuk and D. Simmons-Duffin, Harmonic Analysis and Mean Field Theory, JHEP 10 (2019) 217 [arXiv:1809.05111] [INSPIRE].
M. Hogervorst and B.C. van Rees, Crossing symmetry in alpha space, JHEP 11 (2017) 193 [arXiv:1702.08471] [INSPIRE].
D. Rutter and B.C. Van Rees, Applications of Alpha Space, JHEP 12 (2020) 048 [arXiv:2003.07964] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
S. Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions, SpringerBriefs in Physics, Springer, Heidelberg Germany (2016) [arXiv:1601.05000] [INSPIRE].
D. Simmons-Duffin, The Conformal Bootstrap, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, Boulder U.S.A. (2017), pg. 1 [arXiv:1602.07982] [INSPIRE].
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE Convergence in Conformal Field Theory, Phys. Rev. D 86 (2012) 105043 [arXiv:1208.6449] [INSPIRE].
M. Hogervorst and S. Rychkov, Radial Coordinates for Conformal Blocks, Phys. Rev. D 87 (2013) 106004 [arXiv:1303.1111] [INSPIRE].
L. Di Pietro, V. Gorbenko and S. Komatsu, Cosmological Correlators at Finite Coupling, to appear.
D. Anninos, F. Denef, Y.T.A. Law and Z. Sun, Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions, JHEP 01 (2022) 088 [arXiv:2009.12464] [INSPIRE].
D.L. Jafferis, A. Lupsasca, V. Lysov, G.S. Ng and A. Strominger, Quasinormal quantization in de Sitter spacetime, JHEP 01 (2015) 004 [arXiv:1305.5523] [INSPIRE].
D. Anninos and T. Anous, A de Sitter Hoedown, JHEP 08 (2010) 131 [arXiv:1002.1717] [INSPIRE].
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive moments for scattering amplitudes, Phys. Rev. D 104 (2021) 036006 [arXiv:2011.00037] [INSPIRE].
A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry, JHEP 05 (2021) 255 [arXiv:2011.02400] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories, JHEP 05 (2021) 280 [arXiv:2011.02957] [INSPIRE].
A. Sinha and A. Zahed, Crossing Symmetric Dispersion Relations in Quantum Field Theories, Phys. Rev. Lett. 126 (2021) 181601 [arXiv:2012.04877] [INSPIRE].
L.-Y. Chiang, Y.-t. Huang, W. Li, L. Rodina and H.-C. Weng, Into the EFThedron and UV constraints from IR consistency, arXiv:2105.02862 [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Sharp Boundaries for the Swampland, JHEP 07 (2021) 110 [arXiv:2102.08951] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, AdS bulk locality from sharp CFT bounds, JHEP 11 (2021) 164 [arXiv:2106.10274] [INSPIRE].
A. Guerrieri, J. Penedones and P. Vieira, Where Is String Theory in the Space of Scattering Amplitudes?, Phys. Rev. Lett. 127 (2021) 081601 [arXiv:2102.02847] [INSPIRE].
S. Kundu, Swampland conditions for higher derivative couplings from CFT, JHEP 01 (2022) 176 [arXiv:2104.11238] [INSPIRE].
M. Gillioz, Momentum-space conformal blocks on the light cone, JHEP 10 (2018) 125 [arXiv:1807.07003] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping Mixed Correlators in the 3D Ising Model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].
E. D’Hoker and D.Z. Freedman, General scalar exchange in AdS(d+1), Nucl. Phys. B 550 (1999) 261 [hep-th/9811257] [INSPIRE].
E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
S. El-Showk and K. Papadodimas, Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].
U. Moschella and R. Schaeffer, Quantum theory on Lobatchevski spaces, Class. Quant. Grav. 24 (2007) 3571 [arXiv:0709.2795] [INSPIRE].
L. Cornalba, M.S. Costa and J. Penedones, Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling, JHEP 06 (2008) 048 [arXiv:0801.3002] [INSPIRE].
M.S. Costa, V. Gonçalves and J. Penedones, Spinning AdS Propagators, JHEP 09 (2014) 064 [arXiv:1404.5625] [INSPIRE].
D. Krotov and A.M. Polyakov, Infrared Sensitivity of Unstable Vacua, Nucl. Phys. B 849 (2011) 410 [arXiv:1012.2107] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
M. Hogervorst, S. Rychkov and B.C. van Rees, Unitarity violation at the Wilson-Fisher fixed point in 4-ϵ dimensions, Phys. Rev. D 93 (2016) 125025 [arXiv:1512.00013] [INSPIRE].
A.A. Starobinsky, In Fundamental Interactions, MGPI Press, Moscow USSR (1984).
A.A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background, Phys. Rev. D 50 (1994) 6357 [astro-ph/9407016] [INSPIRE].
M. Mirbabayi, Markovian dynamics in de Sitter, JCAP 09 (2021) 038 [arXiv:2010.06604] [INSPIRE].
T. Cohen, D. Green, A. Premkumar and A. Ridgway, Stochastic Inflation at NNLO, JHEP 09 (2021) 159 [arXiv:2106.09728] [INSPIRE].
F. Gliozzi, More constraining conformal bootstrap, Phys. Rev. Lett. 111 (2013) 161602 [arXiv:1307.3111] [INSPIRE].
S. El-Showk and M.F. Paulos, Extremal bootstrapping: go with the flow, JHEP 03 (2018) 148 [arXiv:1605.08087] [INSPIRE].
E. Mottola, Particle Creation in de Sitter Space, Phys. Rev. D 31 (1985) 754 [INSPIRE].
B. Allen, Vacuum States in de Sitter Space, Phys. Rev. D 32 (1985) 3136 [INSPIRE].
Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitationally prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
X. Dong, X.-L. Qi, Z. Shangnan and Z. Yang, Effective entropy of quantum fields coupled with gravity, JHEP 10 (2020) 052 [arXiv:2007.02987] [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].
D. Baumann, D. Green and T. Hartman, Dynamical Constraints on RG Flows and Cosmology, JHEP 12 (2019) 134 [arXiv:1906.10226] [INSPIRE].
G. Konstantinidis, R. Mahajan and E. Shaghoulian, Late-time Structure of the Bunch-Davies FRW Wavefunction, JHEP 10 (2016) 103 [arXiv:1608.06163] [INSPIRE].
P. McFadden and K. Skenderis, Cosmological 3-point correlators from holography, JCAP 06 (2011) 030 [arXiv:1104.3894] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Holography for inflation using conformal perturbation theory, JHEP 04 (2013) 047 [arXiv:1211.4550] [INSPIRE].
J. Chluba, J. Hamann and S.P. Patil, Features and New Physical Scales in Primordial Observables: Theory and Observation, Int. J. Mod. Phys. D 24 (2015) 1530023 [arXiv:1505.01834] [INSPIRE].
S.B. Giddings and M.S. Sloth, Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes, Phys. Rev. D 86 (2012) 083538 [arXiv:1109.1000] [INSPIRE].
L. Senatore and M. Zaldarriaga, The constancy of ζ in single-clock Inflation at all loops, JHEP 09 (2013) 148 [arXiv:1210.6048] [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].
M. Mirbabayi and M. Simonović, Weinberg Soft Theorems from Weinberg Adiabatic Modes, arXiv:1602.05196 [INSPIRE].
R.Z. Ferreira, M. Sandora and M.S. Sloth, Patient Observers and Non-perturbative Infrared Dynamics in Inflation, JCAP 02 (2018) 055 [arXiv:1703.10162] [INSPIRE].
S. Dubovsky, L. Senatore and G. Villadoro, Universality of the Volume Bound in Slow-Roll Eternal Inflation, JHEP 05 (2012) 035 [arXiv:1111.1725] [INSPIRE].
V. Assassi, D. Baumann and D. Green, Symmetries and Loops in Inflation, JHEP 02 (2013) 151 [arXiv:1210.7792] [INSPIRE].
A. Kehagias and A. Riotto, Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter, Nucl. Phys. B 864 (2012) 492 [arXiv:1205.1523] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Cosmological Event Horizons, Thermodynamics, and Particle Creation, Phys. Rev. D 15 (1977) 2738 [INSPIRE].
N. Goheer, M. Kleban and L. Susskind, The Trouble with de Sitter space, JHEP 07 (2003) 056 [hep-th/0212209] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [INSPIRE].
L. Susskind, de Sitter Holography: Fluctuations, Anomalous Symmetry, and Wormholes, Universe 7 (2021) 464 [arXiv:2106.03964] [INSPIRE].
M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2004) 393 [hep-th/0407125] [INSPIRE].
M. Alishahiha, A. Karch and E. Silverstein, Hologravity, JHEP 06 (2005) 028 [hep-th/0504056] [INSPIRE].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and \( T\overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE].
Simons Observatory collaboration, The Simons Observatory: Science goals and forecasts, JCAP 02 (2019) 056 [arXiv:1808.07445] [INSPIRE].
CMB-S4 collaboration, CMB-S4: Forecasting Constraints on Primordial Gravitational Waves, Astrophys. J. 926 (2022) 54 [arXiv:2008.12619] [INSPIRE].
D.J. Schlegel et al., Astro2020 APC White Paper: The MegaMapper: a z > 2 Spectroscopic Instrument for the Study of Inflation and Dark Energy, arXiv:1907.11171 [INSPIRE].
O. Dore and SPHEREx Science Team, SPHEREx: Probing the Physics of Inflation with an All-Sky Spectroscopic Galaxy Survey, in American Astronomical Society Meeting Abstracts. Vol. 231, AAS Publishing, Washington U.S.A. (2018), pg. 354.
Planck collaboration, Planck 2018 results. IX. Constraints on primordial non-Gaussianity, Astron. Astrophys. 641 (2020) A9 [arXiv:1905.05697] [INSPIRE].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
T. Banks and W. Fischler, An Holographic cosmology, hep-th/0111142 [INSPIRE].
C. Behan, L. Rastelli, S. Rychkov and B. Zan, Long-range critical exponents near the short-range crossover, Phys. Rev. Lett. 118 (2017) 241601 [arXiv:1703.03430] [INSPIRE].
I.M. Gel’fand, M.I. Graev and N.Y. Vilenkin, Generalized functions, Volume 5: Integral Geometry and Representation Theory, Academic Press, New York U.S.A. (1966).
T. Hertog and J. Hartle, Holographic No-Boundary Measure, JHEP 05 (2012) 095 [arXiv:1111.6090] [INSPIRE].
A. Higuchi, D. Marolf and I.A. Morrison, On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT, Phys. Rev. D 83 (2011) 084029 [arXiv:1012.3415] [INSPIRE].
J. Bros, U. Moschella and J.P. Gazeau, Quantum field theory in the de Sitter universe, Phys. Rev. Lett. 73 (1994) 1746 [INSPIRE].
J. Bros and U. Moschella, Two point functions and quantum fields in de Sitter universe, Rev. Math. Phys. 8 (1996) 327 [gr-qc/9511019] [INSPIRE].
J. Bros and U. Moschella, Fourier analysis and holomorphic decomposition on the one sheeted hyperboloid, math-ph/0311052 [INSPIRE].
K. Nguyen, de Sitter-invariant States from Holography, Class. Quant. Grav. 35 (2017) 225006 [arXiv:1710.04675] [INSPIRE].
C. Sleight and M. Taronna, From dS to AdS and back, JHEP 12 (2021) 074 [arXiv:2109.02725] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2108.01695
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Di Pietro, L., Gorbenko, V. & Komatsu, S. Analyticity and unitarity for cosmological correlators. J. High Energ. Phys. 2022, 23 (2022). https://doi.org/10.1007/JHEP03(2022)023
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)023