Toolkit for scalar fields in universes with finite-dimensional Hilbert space
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DrAshmeet Singh(Caltech)
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Europe/Paris
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Description
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 will re-examine some basic constructions in quantum mechanics through the lens of generalized Pauli operators which offer a natural construction to think about finite-dimensional conjugate variables. We will introduce a set of numerical and conceptual tools to describe scalar fields with finite-dimensional Hilbert spaces, and to study their behavior in expanding cosmological backgrounds. With an eye towards dark energy and to better understand the role of quantum mechanics in cosmological evolution, we will demonstrate that the vacuum energy density of the finite-dimensional field is dynamical, suppressed compared to its standard infinite-dimensional counterpart, and can even decay between two constant epochs. These results rely on a number of non-trivial modeling 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.