Final answer:
No, we cannot determine a center of the universe's expansion, because the universe has no center. Observations of cosmic microwave background radiation and galactic redshifts support the idea of a uniformly expanding universe, where every point appears as if it's the center of the expansion.
Step-by-step explanation:
The correct answer to whether we can determine the center of the universe's expansion if there is no observable edge is No, because the universe has no center. The Big Bang model describes the universe as expanding from a hot and dense initial condition at a specific point in time, roughly 13.8 billion years ago. However, it did not expand into an existing space with a central point; rather, space itself is expanding. This means every region of the universe looks like it is the center, because everything is moving away from everything else. This is confirmed through observations of the cosmic microwave background radiation (CMB) and galactic red shifts.
If the universe is infinite, or even if it is finite but unbounded like the surface of a sphere, it would mean that there is no particular special point that can be considered the center. The balloon analogy, where the surface of the balloon represents a two-dimensional universe, shows that as the balloon inflates, every point on the balloon's surface moves away from every other point, with no center of expansion on the surface itself. Thus, any observer, no matter where they are located, will see objects moving away from them, as if they were at the center of the expansion.