Holographic cosmology at finite time
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We investigate Cauchy Slice Holography in de Sitter spacetime. By performing a T2 deformation of a (bottom-up) dS/CFT model, we obtain a holographic theory living on flat Cauchy slices of de Sitter, for which time is an emergent dimension, associated with an RG flow. In this T2-deformed field theory, the dS/CFT is an IR fixed point rather than a UV fixed point, potentially affecting discussions of naturalness. As in the case of AdS/CFT, the terms in the T2 deformation depend on the dimension and the bulk matter sector; in this article we consider gravity, plus optionally a scalar field of arbitrary mass. We compute scalar and graviton two-point correlation functions in the deformed boundary theory, and demonstrate precise agreement with finite-time wavefunction coefficients, which we calculate independently on the bulk side. The results are analytic in the scalar field dimension ∆, and may therefore be continued to arbitrary generic values, including the principal series. Although many aspects of the calculations are similar to the AdS/CFT case, some new features arise due to the complex phases which appear in cosmology. Our calculations confirm previous expectations that the holographic counterterms are purely imaginary, when expressed in terms of wavefunction coefficients. But cosmological correlators, calculated by the Born rule, are shifted in a more complicated and nonlinear way.
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Acknowledgements: AT is grateful to Victor Gorbenko for helpful discussions. GAR thanks Rifath Khan for initial collaboration. The authors are also grateful to Ahmed Almheiri, Matthew Blacker, Laurent Freidel, Monica Guica, Tom Hartman, Simon Lin, Juan Maldacena. Paul McFadden, Vasudev Shyam, Eva Silverstein, Kostas Skenderis, and Ronak Soni for helpful discussions. GAR was supported by a Harding Distinguished Postgraduate Scholarship at the University of Cambridge, as well as funding from Okinawa Institute of Science and Technology Graduate University and support from ID# 62312 grant from the John Templeton Foundation, as part of ‘The Quantum Information Structure of Spacetime’ Project (QISS). The opinions expressed in this project are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. GAR, AT and AW were supported by the AFOSR grant FA9550-19-1-0260 “Tensor Networks and Holographic Spacetime”. GAR and AW are grateful for the hospitality of the KITP in early 2020, during the “Gravitational Holography” program, during which this work was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. AW was also supported by the STFC grant ST/P000681/1 “Particles, Fields and Extended Objects”, and by the subsequent STFC grant ST/X000664/1 “Quantum Fields, Quantum Gravity and Quantum Particles. AT was supported in part by the Heising-Simons Foundation, the Simons Foundation, the Bell Burnell Graduate Scholarship Fund, the Cavendish (University of Cambridge) and a KITP Graduate fellowship. AT also acknowledges support from the SNF starting grant “The Fundamental Description of the Expanding Universe. AT also gratefully acknowledges hospitality from the Perimeter Institute while working on this article. AW was also partly supported by NSF grant PHY-2207584 while working on this paper during his sabbatical at the IAS. Data Availability Statement. This article has no associated data or the data will not be deposited. Code Availability Statement. This article has no associated code or the code will not be deposited.
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1029-8479
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Science and Technology Facilities Council (ST/X000664/1)