The temperature across the Universe is the same.
The Universe contained the heat of the Big Bang flame. Because it had nowhere to go, it is still with us today. The strange thing is that its temperature – 2.725°C above absolute zero (–270°C), the lowest temperature imaginable – is nearly constant throughout. However, if we view cosmic expansion as a backward movie, we can see that sections of the Universe that are now on opposite sides of the sky were not in contact when the fireball of radiation burst free of matter. In other words, from the beginning of time, there hasn't been enough time for heat to move between them for the temperature to equalize. Astronomers remedy this by claiming that the Universe was considerably smal