Re: Flatness & an accelerating Universe

Hi, Edward,
The answer to your question lies in the difference between the comoving distance and the proper distance in an expanding universe.

The comoving distance between two (very distant) objects does not change as the universe expands---the coordinate system expands along with the expansion of the underlying space. The proper distance is what you would measure with a ruler and it does change with expansion. An often quoted example is that of a balloon with marks drawn on the surface---as the balloon expands, the proper distance between the marks increases, but the comoving distance stays the same. This means that the comoving density of the marks stays the same during the expansion, while the proper density decreases.

The test for curvature mentioned in Gamow's book applies to the comoving distance, not the proper distance. Hence the expansion, whether accelerated or not, has no effect on the result. The universe is, in fact, flat and accelerating.

To visualize a flat accelerating universe, think of a flat rubber sheet with a uniform square grid of dots drawn on the surface. You can keep stretching it with any velocity and acceleration, and the number of dots within a comoving distance will always increase with exactly the square of the comoving distance.

Vit