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Future boundary conditions in de Sitter space. (English) Zbl 1309.81306

Summary: We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary \({\mathcal{I}^{+}}\) is deformed by the flux of gravitational radiation. We however impose an unconventional future “Dirichlet” boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at \({\mathcal{I}^{+}}\). This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any normalizable de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.

MSC:

81V22 Unified quantum theories
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C35 Gravitational waves
83F05 Relativistic cosmology
35G15 Boundary value problems for linear higher-order PDEs

References:

[1] G. Gibbons and S. Hawking, Cosmological event horizons, thermodynamics and particle creation, Phys. Rev.D 15 (1977) 2738 [INSPIRE].
[2] R. Bousso, Positive vacuum energy and the N bound, JHEP11 (2000) 038 [hep-th/0010252] [INSPIRE]. · Zbl 0990.83513 · doi:10.1088/1126-6708/2000/11/038
[3] M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc.743 (2005) 393 [hep-th/0407125] [INSPIRE]. · doi:10.1063/1.1848341
[4] T. Banks, Some thoughts on the quantum theory of de Sitter space, astro-ph/0305037 [INSPIRE].
[5] T. Banks, Pedagogical notes on black holes, de Sitter space and bifurcated horizons, arXiv:1007.4003 [INSPIRE].
[6] N. Goheer, M. Kleban and L. Susskind, The trouble with de Sitter space, JHEP07 (2003) 056 [hep-th/0212209] [INSPIRE]. · doi:10.1088/1126-6708/2003/07/056
[7] A. Castro, N. Lashkari and A. Maloney, A de Sitter farey tail, Phys. Rev.D 83 (2011) 124027 [Addendum ibid.D 84 (2011) 089904] [arXiv:1103.4620] [INSPIRE].
[8] T. Banks, W. Fischler and S. Paban, Recurrent nightmares? Measurement theory in de Sitter space, JHEP12 (2002) 062 [hep-th/0210160] [INSPIRE]. · doi:10.1088/1126-6708/2002/12/062
[9] E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [INSPIRE]. · Zbl 1054.83013
[10] D. Anninos, G.S. Ng and A. Strominger, Asymptotic symmetries and charges in de Sitter space, Class. Quant. Grav.28 (2011) 175019 [arXiv:1009.4730] [INSPIRE]. · Zbl 1225.83019 · doi:10.1088/0264-9381/28/17/175019
[11] H. Bondi, M. van der Burg and A. Metzner, Gravitational waves in general relativity. VII. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond.A 269 (1962) 21 [INSPIRE]. · Zbl 0106.41903
[12] R. Sachs, Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond.A 270 (1962) 103 [INSPIRE]. · Zbl 0101.43605
[13] L.A. Tamburino and J.H. Winicour, Gravitational fields in finite and conformal Bondi frames, Phys. Rev.150 (1966) 1039 [INSPIRE]. · doi:10.1103/PhysRev.150.1039
[14] J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP05 (2003) 013 [astro-ph/0210603] [INSPIRE]. · doi:10.1088/1126-6708/2003/05/013
[15] P. McFadden and K. Skenderis, Holography for cosmology, Phys. Rev.D 81 (2010) 021301 [arXiv:0907.5542] [INSPIRE].
[16] F. Larsen, J.P. van der Schaar and R.G. Leigh, De Sitter holography and the cosmic microwave background, JHEP04 (2002) 047 [hep-th/0202127] [INSPIRE]. · doi:10.1088/1126-6708/2002/04/047
[17] A. Strominger, The dS/CFT correspondence, JHEP10 (2001) 034 [hep-th/0106113] [INSPIRE]. · doi:10.1088/1126-6708/2001/10/034
[18] A. Strominger, Inflation and the dS/CFT correspondence, JHEP11 (2001) 049 [hep-th/0110087] [INSPIRE]. · doi:10.1088/1126-6708/2001/11/049
[19] J. Maldacena, Einstein gravity from conformal gravity, arXiv:1105.5632 [INSPIRE]. · Zbl 1258.83002
[20] E. Schrödinger, Expanding universes, Cambridge University Press, Cambridge U.K. (1956). · Zbl 0075.21603
[21] M.K. Parikh, I. Savonije and E.P. Verlinde, Elliptic de Sitter space: dS/Z2, Phys. Rev.D 67 (2003) 064005 [hep-th/0209120] [INSPIRE]. · Zbl 1222.83043
[22] A. Folacci and N.G. Sanchez, Quantum Field Theory and the ‘elliptic interpretation’ of de Sitter space-time, Nucl. Phys.B 294 (1987) 1111 [INSPIRE].
[23] G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP02 (2004) 008 [hep-th/0310281] [INSPIRE]. · doi:10.1088/1126-6708/2004/02/008
[24] L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev.D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
[25] B. Allen, Vacuum states in de Sitter space, Phys. Rev.D 32 (1985) 3136 [INSPIRE].
[26] M. Spradlin, A. Strominger and A. Volovich, Les Houches lectures on de Sitter space, hep-th/0110007 [INSPIRE].
[27] R. Bousso, A. Maloney and A. Strominger, Conformal vacua and entropy in de Sitter space, Phys. Rev.D 65 (2002) 104039 [hep-th/0112218] [INSPIRE].
[28] H. Kodama and A. Ishibashi, Master equations for perturbations of generalized static black holes with charge in higher dimensions, Prog. Theor. Phys.111 (2004) 29 [hep-th/0308128] [INSPIRE]. · Zbl 1073.83029 · doi:10.1143/PTP.111.29
[29] A.A. Starobinsky, Isotropization of arbitrary cosmological expansion given an effective cosmological constant, JETP Lett.37 (1983) 66 [INSPIRE].
[30] D. Anninos and T. Hartman, Holography at an extremal de Sitter horizon, JHEP03 (2010) 096 [arXiv:0910.4587] [INSPIRE]. · Zbl 1271.83038 · doi:10.1007/JHEP03(2010)096
[31] D. Anninos and T. Anous, A de Sitter hoedown, JHEP08 (2010) 131 [arXiv:1002.1717] [INSPIRE]. · Zbl 1290.83030 · doi:10.1007/JHEP08(2010)131
[32] D. Anninos, S. de Buyl and S. Detournay, Holography for a de Sitter-Esque geometry, JHEP05 (2011) 003 [arXiv:1102.3178] [INSPIRE]. · Zbl 1296.83022 · doi:10.1007/JHEP05(2011)003
[33] M. Spradlin and A. Volovich, Vacuum states and the S matrix in dS/CFT, Phys. Rev.D 65 (2002) 104037 [hep-th/0112223] [INSPIRE].
[34] D. Harlow and D. Stanford, Operator dictionaries and wave functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
[35] H. Kodama and M. Sasaki, Cosmological perturbation theory, Prog. Theor. Phys. Suppl.78 (1984) 1 [INSPIRE], appendix D. · doi:10.1143/PTPS.78.1
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