Towards a quantum theory of de Sitter space

TL;DR

The paper proposes a holographic, finite-N framework for quantum de Sitter space in four dimensions, where both particle states and Schwarzschild–de Sitter black holes arise as excitations of fermionic matrices. A static-Hamiltonian H and an emergent P0 govern the system, yielding a thermal de Sitter background and particle masses, with black holes encoded as specific matrix blocks and entropy deficits matching dS entropy. The construct relies on a conjectured Grassmann-based limit to a Fock space of superparticles, together with a fuzzy-sphere discretization of the cosmological horizon and a block-structure dictionary for multiparticle states. Finite-N corrections are analyzed to connect to flat-space SUSY and propose scaling laws for gravitino masses, while outlining concrete future steps to derive an interacting S-matrix and fully dynamical theory. The work provides a principled, kinematic bridge between holographic cosmology and microphysical particle states, pointing toward a deeper string/M-theory embedding.

Abstract

We describe progress towards constructing a quantum theory of de Sitter space in four dimensions. In particular we indicate how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite number of fermionic oscillators. The results about particle states depend on a conjecture about algebras of Grassmann variables, which we state, but do not prove.