Three pieces of evidence of universe expansion that support the Big Bang Theory are as follows:
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The first piece of evidence, which Edwin Hubble discovered, is that galaxies are moving away from us in all directions, with their recessional velocity proportional to their distance. This observation is known as Hubble's Law and indicates that the universe is expanding.
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The second piece of evidence is the change in universal temperature. The temperature of the universe has been cooling over time, consistent with the predictions of the Big Bang Theory. Currently, the average temperature of the universe is about 2.7 Kelvin, which indicates it was much hotter in its early stages. This cooling supports the idea of an expanding universe.
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The third piece of evidence is that Cosmic Microwave Background radiation is found uniformly throughout the universe, providing a relic from the early hot and dense state of the universe. This faint afterglow from the Big Bang supports the notion that the universe has been expanding and cooling over time.
Together, these pieces of evidence provide strong support for the Big Bang Theory and our understanding of the universe's evolution.