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There are a couple of problems with the standard Big Bang model. The first is called the flatness problem---why is the universe density so nearly at the critical density or put another way, why is the universe so flat? Currently, the universe is so well-balanced between the positively-curved closed universe and the negatively-curved open universe that astronomers have a hard time figuring out which model to choose. Of all the possibilities from very positively-curved (very high density) to very negatively-curved (very low density), the current nearly flat condition is definitely a special case. The balance would need to have been even finer nearer the time of the Big Bang because any deviation from perfect balance gets magnified over time. For example, if the universe density was slightly greater than the critical density a billion years after the Big Bang, the universe would have recollapsed by now.
Consider the analogy of the difficulty of shooting an arrow at a small target from a distance away. If your angle of shooting is a little off, the arrow misses the target. The permitted range of deviation from the true direction gets narrower and narrower as you move farther and farther away from the target. The earlier in time the universe's curvature became fixed, the more finely tuned the density must have been to make the universe's current density be so near the critical density. If the curvature of the universe was just a few percent off from perfect flatness within a few seconds after the Big Bang, the universe would have either recollapsed before fusion ever began or the universe would expanded so much that it would seem to be devoid of matter. It appears that the density/curvature was very finely tuned.
The second problem with the standard Big Bang model is the horizon problem---why does the universe, particularly the microwave background, look the same in all directions? The only way for two regions to have the same conditions (e.g., temperature), is that they are close enough to each other for information to be exchanged between them so that they can equilibrate to a common state. The fastest speed that information can travel is the speed of light. If two regions are far enough apart that light has not had enough time to travel between the regions, the regions are isolated from each other. The regions are said to be beyond their horizons because the regions cannot be in contact with each other (recall the term event horizon in the discussion about black holes).
The photons from the microwave background have been travelling nearly the age of the universe to reach us right now. Those photons have certainly not had the time to travel across the entire universe to the regions in the opposite direction from which they came. Yet when astronomers look in the opposite directions, they see that the microwave background looks the same to very high precision. How can the regions be so precisely the same if they are beyond each other's horizons? Running the expansion backward, astronomers find that regions even a degree apart in angular separation on our sky would have been beyond each other's horizons at the time the microwave background was produced.