Abstract
We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff- and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi’s norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state.
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Acknowledgments
We are grateful to Simon Caron-Huot, Abhijit Gadde, Rifath Khan, Alex Maloney, Ashoke Sen and Sandip Trivedi for helpful discussions. We also acknowledge several discussions with the string theory group at ICTS-TIFR. S.R. would like to acknowledge the hospitality of the 12th Joburg Workshop on string theory, the Abu Dhabi meeting in theoretical physics and the workshop on observables in quantum gravity (IISER Mohali) where preliminary versions of these results were presented. S.R. is partially supported by a Swarnajayanti fellowship, DST/SJF/PSA-02/2016-17, of the Department of Science and Technology. J.C. is supported by the Simons Collaboration on Nonperturbative Bootstrap. Research at ICTS-TIFR is supported by the Department of Atomic Energy, Government of India, under Project Identification Nos. RTI4001.
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Chakraborty, T., Chakravarty, J., Godet, V. et al. Holography of information in de Sitter space. J. High Energ. Phys. 2023, 120 (2023). https://doi.org/10.1007/JHEP12(2023)120
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DOI: https://doi.org/10.1007/JHEP12(2023)120