DECOHERENT SUBREGION COSMOLOGY, A Framework for Emergent Spacetime, Time, and Entropy

We propose a cosmological framework in which the observable universe is a decoherent subregion of a larger quantum system — the Universal Wavefunction or Cloud — existing as a pure state in an abstract Hilbert space with zero von Neumann entropy. Classical spacetime, the arrow of time, the apparent low initial entropy, and the full expansion history are emergent properties of the algebraic structure of Hilbert space as experienced from within a decoherent subregion.

The foundational insight is phenomenological: our universe is a partition of the universal wavefunction, precisely as a vacuum fluctuation is a partition of the vacuum field. A vacuum fluctuation separates a local region from the ground state of the field. Our subregion separates a local algebraic structure from the ground state of the universal wavefunction. In both cases, the partition has an entropy — the von Neumann entropy of the reduced state of the partition relative to its complement. That entropy is zero at the beginning and end of the partition's existence, and non-zero during its existence.

The arrow of time within the partition is the direction in which the von Neumann entropy of the partition is changing. When S(ρ_S) is larger along the delta chain, the partition is more separated from the Cloud. When S(ρ_S) is smaller along the delta chain, the partition is closer to the Cloud. The arrow of time that internal observers experience is the direction along the delta chain in which local S(ρ_S) is larger — not backward-looking, always locally forward. This formulation requires no energy, no Hamiltonian, no external temporal parameter, and no statistical measure over the space of states. It requires only the algebraic structure of the partition and its complement.

A concrete falsifiable prediction follows: the dark energy equation of state w(z), currently measured by DESI DR2 as rising from values below −1, must continue rising monotonically toward zero and subsequently positive values as the subregion's entropy begins to decrease toward its final state of zero.