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Toolkit for scalar fields in universes with finite-dimensional Hilbert space

Friedrich, Oliver and Singh, Ashmeet and Doré, Olivier (2022) Toolkit for scalar fields in universes with finite-dimensional Hilbert space. Classical and Quantum Gravity, 39 (23). Art. No. 235012. ISSN 0264-9381. doi:10.1088/1361-6382/ac95f0.

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The holographic principle suggests that the Hilbert space of quantum gravity is locally finite-dimensional. Motivated by this point-of-view, and its application to the observable Universe, we introduce a set of numerical and conceptual tools to describe scalar fields with finite-dimensional Hilbert spaces, and to study their behaviour in expanding cosmological backgrounds. These tools include accurate approximations to compute the vacuum energy of a field mode k as a function of the dimension dₖ of the mode Hilbert space, as well as a parametric model for how that dimension varies with |k|. We show that the maximum entropy of our construction momentarily scales like the boundary area of the observable Universe for some values of the parameters of that model. And we find that the maximum entropy generally follows a sub-volume scaling as long as dₖ decreases with |k|. We also demonstrate that the vacuum energy density of the finite-dimensional field is dynamical, and decays between two constant epochs in our fiducial construction. These results rely on a number of non-trivial modelling choices, but our general framework may serve as a starting point for future investigations of the impact of finite-dimensionality of Hilbert space on cosmological physics.

Item Type:Article
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URLURL TypeDescription
Friedrich, Oliver0000-0001-6120-4988
Singh, Ashmeet0000-0002-4404-1416
Doré, Olivier0000-0002-5009-7563
Additional Information:We are thankful to ChunJun (Charles) Cao, Sean Carroll, Steffen Hagstotz and Cora Uhlemann for helpful comments and discussions. OF gratefully acknowledges support by the Kavli Foundation and the International Newton Trust through a Newton-Kavli-Junior Fellowship, by Churchill College Cambridge through a postdoctoral By-Fellowship and by the Ludwig-Maximilians Universität through a Karl-Schwarzschild-Fellowship. AS acknowledges the generous support of the Heising-Simons Foundation. Part of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. We indebted to the invaluable work of the teams of the public python packages NumPy, SciPy, mpmath and Matplotlib. And we would like to thank the anonymous journal referees for their comments and encouraging feedback.
Funding AgencyGrant Number
Kavli FoundationUNSPECIFIED
Churchill CollegeUNSPECIFIED
Ludwig-Maximilians UniversitätUNSPECIFIED
Heising-Simons FoundationUNSPECIFIED
Issue or Number:23
Record Number:CaltechAUTHORS:20221219-417430800.22
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ID Code:118495
Deposited By: Research Services Depository
Deposited On:20 Jan 2023 21:41
Last Modified:22 Jan 2023 21:02

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