I just want to point out that the terms "open" and "closed" are used with different meanings in cosmology and thermodynamics.

In cosmology, the terms closed, flat, and open are used to refer to spatial cross-sections that have positive, zero, or negative curvature respectively. Closed spaces have a finite volume, flat and open spaces have infinite volume.

In thermodynamics, the terms open and closed refer to systems that can or cannot exchange energy and momentum with other systems respectively.

There is no reason why a universe cannot be both closed thermodynamically and either open or flat spatially. I hope this clears up some confusion.

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