### 4. INFLATION AND THE VERY SPECIAL BANG

Once inflation has been described, it is not hard to see how it produces just the special kind of bang that was discussed earlier.

Consider first the horizon problem, the difficulty of understanding the large-scale homogeneity of the Universe in the context of the traditional Big Bang theory. Suppose we trace back through time the observed region of the Universe, which has a radius today of about 10 billion light-years. As we trace its history back to the end of the inflationary period, our description is identical to what it would be in the traditional Big Bang theory, since the two theories agree exactly for all times after the end of inflation. In the inflationary theory, however, the region undergoes a tremendous spurt of expansion during the inflationary era. It follows that the region was incredibly small before the spurt of expansion began - 1025 or more times smaller in radius than in the traditional theory. (Note that I am not saying that Universe as a whole was very small. The inflationary model makes no statement about the size of the Universe as a whole, which might in fact be infinite.)

Because the region was so small, there was plenty of time for it to come to a uniform temperature, by the same mundane processes by which a cup of hot coffee cools to room temperature as it sits on a table. So in the inflationary model, the uniform temperature was established before inflation took place, in an extremely small region. The process of inflation then stretched this region to become large enough to encompass the entire observed Universe. The uniformity is preserved by this expansion, because the laws of physics are (we assume) the same everywhere.

The inflationary model also provides a simple resolution for the flatness problem, the fine-tuning required of the mass density of the early Universe. Recall that the ratio of the actual mass density to the critical density is called omega, and that the problem arose because the condition = 1 is unstable: omega is always driven away from one as the Universe evolves, making it difficult to understand how its value today can be in the vicinity of one.

During the inflationary era, however, the peculiar nature of the false vacuum state results in some important sign changes in the equations that describe the evolution of the Universe. During this period, as we have discussed, the force of gravity acts to accelerate the expansion of the Universe rather than to retard it. It turns out that the equation governing the evolution of omega also has a crucial change of sign: during the inflationary period the Universe is driven very quickly and very powerfully towards a critical mass density. This effect can he understood if one accepts from general relativity the relationship between a critical mass density and the geometric flatness of space. The huge expansion factor of inflation drives the Universe toward flatness for the same reason that the Earth appears flat, even though in is really round. A small piece of any curved space, if magnified sufficiently, will appear flat.

Thus, a short period of inflation can drive the value of omega very accurately to one, no matter where it starts out. There is no longer any need to assume that the initial value of omega was incredibly close to one.

Furthermore, there is a prediction that arises from this behavior. The mechanism that drives omega to one almost always overshoots, which means that even today the mass density should be equal to the critical value to a high degree of accuracy. (If Einstein's cosmological constant is nonzero, this prediction is modified to become + / 3H2 = 1, where H is Hubble's constant.) Thus, the determination of the mass density of the Universe could be a very important test of the inflationary model. Unfortunately, it is very difficult to reliably estimate the mass density of the Universe, since most of the matter in the Universe is "dark," detected only through its gravitational pull on visible matter. Current estimates of omega range from 0.2 to 1.1. Nonetheless, it is likely that this issue can be settled in the near future. The high precision measurements of the microwave background radiation that will be made by the Microwave Anisotropy Probe, scheduled for launch in about 2001, are expected to pin down the value of omega to about 5 percent accuracy.