de Sitter complexity grows linearly in the static patch

The observable Universe has undergone periods of expansion that are well approximated by de Sitter (dS) space. Still lacking is a quantum-mechanical description of dS spacetime, both globally and when restricted to the static patch. We develop a novel prescription, to the best of our knowledge, for computing holographic complexity in the dS static patch to determine its microscopic features. Specifically, we propose that the natural candidate for dS complexity is the volume of extremal “timelike” surfaces restricted to the static patch, anchored to the cosmological horizon or an observer worldline. Our anchoring prescription provides a clear definition of a reference state, overcoming a common ambiguity in prior definitions of de Sitter holographic complexity. The late-time growth of our complexity functional is linear and proportional to the number of degrees of freedom associated with the cosmological horizon and, therefore, does not exhibit hyperfast growth. Our results imply the dS static patch is characterized by a quantum-mechanical system, with a finite-dimensional Hilbert space whose evolution is governed by a chaotic Hamiltonian.