Lessons for Quantum Gravity and Cosmology from the Holographic Principle

The holographic principle suggests that the Hilbert space of quantum gravity hosts fewer physical degrees of freedom than would be implied by conventional quantum field theory. In this talk, I explore the phenomenology of quantum fields with locally finite-dimensional Hilbert spaces, developing both bosonic and fermionic frameworks inspired by holographic bounds. On the bosonic side, I will introduce a set of numerical and conceptual tools to describe scalar fields with finite-dimensional Hilbert spaces to study their behavior in expanding cosmological backgrounds. In parallel, I will discuss a fermionic construction with overlapping, nearly anti-commuting Pauli algebras in high-dimensional Hilbert spaces to emulate holographic behavior. We will explore cosmological implications, such as suppression and dynamical decay of vacuum energy density, finite lifetime of plane waves (for example, of high-energy cosmic neutrinos), and study scaling properties of entropy which yield an effective field theory satisfying the cosmic Bekenstein bound. Beyond being a toolkit for cosmological physics, I will motivate the origins of this program through quantum mereology, i.e. using the idea that effective field theoretic degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions.