Final answer:
The assertion that an accelerating universe can only be open is false. While open universes do expand forever, the possibility of a flat or barely closed universe is supported by recent findings and theories, which also suggest an eternal expansion.
Step-by-step explanation:
The statement that 'The only possible geometry of an accelerating universe is open' is false. In cosmological terms, an open universe is one that has negative curvature, implying it will expand forever. While recent discoveries suggest that the universe is very close to being flat due to the cosmological constant, it does not preclude the possibility of the universe being slightly open or even closed. If the universe has a density less than the critical density, it would indeed be open and expand forever. However, recent evidence and theoretical preference support a universe that is flat on the largest scale. This flat universe is at the critical density and will also expand forever, but without the 'open' negative curvature.
A closed universe is positively curved and if you traveled far enough, you'd end up back where you started, much like circumnavigating the Earth. A flat universe suggests that the space is neither positively nor negatively curved and the expansion will continue indefinitely. Hence, an accelerating universe could be open, flat, or just barely closed, and not solely open as suggested by the question.