The expanding universe

The expansion of the universe means that the average distance between galaxies is increasing. Figure 2.1 shows an early use of a model that helps illustrate the situation. Imagine you live in only two spatial dimensions on the surface of a balloon. Do not ask what is inside or outside the surface - you are confined to your two-dimensional space on the rubber sheet of the balloon. In your two-dimensional space you see a uniform distribution of galaxies: there may be local clustering, as we observe in the real universe, but the mean number of galaxies per unit volume (which in this example is an area) is the same everywhere. As the balloon is blown up the galaxies move apart. Another caution is in order here: the galaxies themselves are not expanding. An observer at rest in any galaxy sees that the other galaxies are moving away, at the same rate in all directions, as if the observer were at the center of expansion of this model universe. But an observer in any

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