String Theory and Inflation
Today, the principles at the heart of inflation theory have a profound impact on the way that string theory is viewed by many physicists. In trying to understand the universe, two major problems remained: the flatness problem and the horizon problem. To solve these two problems, the big bang theory is modified by the inflation theory, which states that the universe expanded rapidly shortly after it was created.
These two problems can be stated simply as:

Horizon problem: The CMBR is essentially the same temperature in all directions.

Flatness problem: The universe appears to have a flat geometry.
The horizon problem (also sometimes called the homogeneity problem) is that no matter which direction you look in the universe, you see basically the same thing, as shown in the figure.
The CMBR temperatures throughout the universe are, to a very high level of measurement, almost exactly the same temperature in every direction. This really shouldn’t be the case, if you think about it more carefully.
If you look in one direction in space, you’re actually looking back in time. The light that hits your eye (or telescope) travels at the speed of light, so it was emitted years ago. This means there’s a boundary of 14 billion (or so) lightyears in all directions. (The boundary is actually farther because space itself is expanding, but you can ignore that for the purposes of this example.)
If there is anything farther away than that, there is no way for it to have ever communicated with us. So you look out with your powerful telescope and can see the CMBR from 14 billion lightyears away (call this Point A).
If you now look 14 billion lightyears in the opposite direction (call this Point B), you see exactly the same sort of CMBR in that direction. Normally, you’d take this to mean that all the CMBR in the universe has somehow diffused throughout the universe, like heating up an oven. Somehow, the thermal information is communicated between Points A and B.
But Points A and B are 28 billion lightyears apart, which means, because no signal can go faster than the speed of light, there’s no way they could have communicated with each other in the entire age of the universe. How did they become the same temperature if there’s no way for heat to transfer between them? This is the horizon problem.
The flatness problem has to do with the geometry of our universe, which appears (especially with recent WMAP evidence) to be a flat geometry, as pictured in this figure. The matter density and expansion rate of the universe appear to be nearly perfectly balanced, even 14 billion years later when minor variations should have grown drastically.
Because this hasn’t happened, physicists need an explanation for why the minor variations haven’t increased dramatically. Did the variations not exist? Did they not grow into largescale variations? Did something happen to smooth them out? The flatness problem seeks a reason why the universe has such a seemingly perfectly flat geometry.