State-to-State Cosmology: a new view on the cosmological arrow of time and the past hypothesis

TL;DR

This paper explores an alternative boundary condition approach for cosmological systems, showing that a typical particle system can spontaneously collapse and expand, which may explain the universe's low-entropy initial state and the arrow of time.

Contribution

It introduces a novel boundary condition framework for cosmology using initial and final states, providing insights into the universe's low-entropy beginning.

Findings

Particles tend to spontaneously collapse into a dense region before expanding.

The behavior suggests a natural explanation for the universe's low-entropy initial state.

Implications for the cosmological arrow of time and boundary condition formulations.

Abstract

Cosmological boundary conditions for particles and fields are often discussed as a Cauchy problem, in which configurations and conjugate momenta are specified on an "initial" time slice. But this is not the only way to specify boundary conditions, and indeed in action-principle formulations we often specify configurations at two times and consider trajectories joining them. Here, we consider a classical system of particles interacting with short range two body interactions, with boundary conditions on the particles' positions for an initial and a final time. For a large number of particles that are randomly arranged into a dilute gas, we find that a typical system trajectory will spontaneously collapse into a small region of space, close to the maximum density that is obtainable, before expanding out again. If generalizable, this has important implications for the cosmological arrow of time, potentially allowing a scenario in which both boundary conditions are generic and also a low-entropy state "initial" state of the universe naturally occurs.