Solution of the Big Bang Problems

An early inflationary period could cure all the problems of the big bang mentioned above. Briefly, the solutions come about as follows.

Solution of the horizon problem: The tremendous expansion means that regions that we see widely separated in the sky now at the horizon were much closer together before inflation and thus could have been in contact by light signals.
Solution of the flatness problem: The tremendous expansion greatly dilutes any initial curvature. Think, for example, of standing on a basketball. It would be obvious that you are standing on a two-dimensional curved surface. Now imagine expanding the basketball to the size of the Earth. As you stand on it now, it will appear to be flat, even though it is actually curved if you could see it from large enough distance. The same idea extended to four-dimensional spacetime accounts for the present flatness (lack of curvature) in the spacetime of the Universe. Out to the greatest distances that we can see the Universe looks flat on large scales, just as the Earth looks approximately flat out to our horizon.
Solution of the monopole problem: The rapid expansion of the Universe tremendously dilutes the concentration of any magnetic monopoles that are produced. Simple calculations indicate that they become so rare in any given volume of space that we would be very unlikely to ever encounter one in an experiment designed to search for them. Nor would they have sufficient density to alter the gravity and thereby the normal expansion of the Universe following inflation.

Thus, at least schematically, the inflationary theory is capable of preserving the correct predictions of the big bang theory, while alleviating some of its difficulties. The following animation summarizes the problems of the big bang and their solution by the inflationary model.

A Clear Prediction
The inflationary theory predicts unequivocally that the observable Universe should globally be almost exactly flat because the rapid expansion dilutes all curvature. It is this prediction that we alluded to earlier when we said that there were theoretical reasons to believe that the Universe should have almost exactly flat geometry. As we have described in other sections of this chapter, there is now strong evidence that the geometry of the Universe is indeed flat, as predicted by inflation.
Unresolved Difficulties
Inflationary theory has the potential to provide a solution for various difficulties in cosmology. However, it also has unresolved issues of its own. For example, the details of what causes inflation are not clearly known. There are many proposals, often revolving around a particular kind of phase transition in the early Universe or the existence of new elementary particles that have not been discovered yet, but there is no uniform agreement on the issue. We may hope that the newer data such as that from high-redshift supernovae and the anisotropy of the cosmic microwave background will help constrain the various versions of inflation and lead to a clear formulation of a single theory.
The Matter-Antimatter Asymmetry Problem, Again
We mentioned earlier a potential solution to the matter-antimatter asymmetry problem involving GUTs. Grand unified theories also produce magnetic monopoles and one of the reasons for introducing the inflationary theory was to inflate away those monopoles (since we don't see monopoles or their influence in our present Universe). But if inflation follows the GUTs phase transition that produces the monopoles and that provides the baryon nonconserving reactions necessary to produce a baryon asymmetry, inflation will also inflate away the baryon asymmetry! Then, when the Universe reheats, no new baryon asymmetry can be introduced by GUTs because the temperature is now below the GUTs scale in the standard inflationary theories.

Thus, in curing the horizon, flatness, and monopole problems, inflation reintroduces the baryon asymmetry problem. This means that if inflation is correct, we do not have a very satisfactory explanation for why there are baryons in the Universe (and since we are made of baryons, of why we exist). The most promising speculation on solving this problem, assuming that inflation is correct, invokes the possibility of new kinds of baryon nonconserving reactions that can occur below the GUTs temperature scale. There are ideas, but no very compelling theory of how this could happen currently exists.