Toolkit for scalar fields in universes with finitedimensional Hilbert space
Abstract
The holographic principle suggests that the Hilbert space of quantum gravity is locally finitedimensional. Motivated by this pointofview, and its application to the observable Universe, we introduce a set of numerical and conceptual tools to describe scalar fields with finitedimensional 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 d _{ k } 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 subvolume scaling as long as d _{ k } decreases with k. We also demonstrate that the vacuum energy density of the finitedimensional field is dynamical, and decays between two constant epochs in our fiducial construction. These results rely on a number of nontrivial modelling choices, but our general framework may serve as a starting point for future investigations of the impact of finitedimensionality of Hilbert space on cosmological physics.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 December 2022
 DOI:
 10.1088/13616382/ac95f0
 arXiv:
 arXiv:2201.08405
 Bibcode:
 2022CQGra..39w5012F
 Keywords:

 quantum cosmology;
 holographic principle;
 finitedimensional Hilbert spaces;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 22 pages + appendix