The Poincaré recurrence theorem is a concept from classical mechanics that states that in a closed system with a finite phase space and under certain conditions, every possible configuration of the system will recur infinitely many times. However, this theorem does not directly apply to the question of the universe's expansion and its potential cycling through every possible configuration.
The Poincaré recurrence theorem assumes a closed and isolated system, which is not necessarily applicable to the universe as a whole. The universe is a complex and dynamic system influenced by various factors, such as dark energy and the initial conditions of the Big Bang. Additionally, the concept of phase space, which is fundamental to the theorem, may not be applicable to the universe's expansion on a cosmological scale.
Furthermore, the current understanding of the universe's expansion suggests that it is accelerating due to the influence of dark energy. If this acceleration continues indefinitely, it may result in an ever-expanding universe without cyclic behavior.
It's important to note that the behavior and fate of the universe are still subjects of ongoing scientific research and investigation. While the Poincaré recurrence theorem is a significant result in classical mechanics, its direct application to the universe's expansion and cyclic behavior remains uncertain.