The Big Bang theory states that the universe is expanding, though it does not explain why the universe should behave in this way. As a result, objects which are subject to no forces should move away from each other. In a uniformly-expanding universe, the rate at which objects move away from each other depends linearly on their distance from each other.
And that linear relationship between distance and radial velocity is just what we see when we look at distant galaxies:
But ... wait a minute. Does this expansion occur on all scales? What about
the distance between two people on opposite sides of the room?
the distance between the Earth and the Sun?
the distance between the Sun and the center of the Milky Way?
the distance between the Milky Way and the Andromeda Galaxy?
If there are "significant" attractive forces between objects, they do not
move away from each other as time goes by. These attractive forces may be
"chemical" forces between important on microscopic,
neighboring molecules or atoms human, and planet-sized
(these are really due to scales
electric forces)
gravitational forces between important on solar-system,
large bodies of matter galaxy, and galaxy-cluster
scales
So the distance between the Earth and Sun has not increased over the
past 4 billion years. Nor does the length of a meterstick grow due to the
expansion of the universe.
Only on the very largest scales, distances between isolated galaxies or
clusters of galaxies, are the attractive forces so weak that the expansion of
the universe is able to move objects apart.
The rate of expansion depends sensitively on the exact amount of
matter in the universe. If the density of matter is high, long-range
gravitational forces can slow down the expansion, or even stop it. If the
density of matter is very low, the expansion will go on forever.
