Horizon Problem
A problem with the simplistic Big Bang theory having to do with the smoothness of the Universe. The Early Universe should have been very random in terms of the temperature and density of different parts of space. This randomness should not have had time to distribute itself more evenly. Yet, this is what is observed in the Universe. The theory of Inflation solves this problem.
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Inspiration
Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run twice as fast as that.