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Yes... The universe is expanding. Everything in the universe is slowly moving farther away from everything else. Even the molecules in your body are drifting away from one another, although too slowly to measure.
This expansion of the universe was first discovered by Edwin Hubble in 1931. Hubble was studying distant galaxies when he made a startling discovery: Every galaxy he looked at seemed to be moving away from our own. With only a few exceptions, like nearby Andromeda, every other spot in the universe was drifting away.
Hubble made this observation by studying the Doppler effect. You may be familiar with the Doppler effect as a phenomenon that affects sound waves (when a loud vehicle passes by you, the pitch suddenly dropes). The same thing happens with light waves. When a galaxy is moving away, the color of the light shifts toward the red end of the spectrum.
Hubble observed this redshifting in every galaxy he looked at, but even more surprisingly he noticed the redshifting was more severe the further away the galaxy was. This meant that galaxies farther away were drifting apart faster than the close galaxies. The only possible conclusion he could draw was that the entire universe was expanding.
Hubble believed that the expansion of the universe was constant, meaning galaxies twice as far away should be moving about twice as fast. But in 1998, another Hubble—the Hubble Space Telescope—made another startling discovery about the universe's expansion. Using the telescope to peer at some of the furthest galaxies in the universe, astronomers discovered that not only is the universe expanding, it's accelerating.
We still don't know why or how the universe is accelerating, but the leading theory is that there's some kind of energy—scientists call it 'dark energy'—pushing everything apart. Perhaps some future Hubble will finally figure out what it is...