Inherent to the Big Bang theory is an expanding universe. Among the evidences:
Einstein's Theory of General Relativity:
One of the first clues that the universe is expanding came from Einstein's theory of general relativity. It predicted that the universe must either be expanding or contracting. First published in 1915, it is now one of the most exhaustively tested principles in all of physics.
The Redshift in Light from Distant Galaxies:
In 1929 Astronomer Edwin Hubble noticed that the light from distance galaxies was shifted to the red of the light spectrum. This observation confirmed that the galaxies were moving away from each other, causing this redshift. His measurements on 40 galaxies constituted the first observational proof of the expansion that Einstein's theory had predicted.
The Hubble Constant:
Since Hubble's time, astronomers have developed sophisticated techniques for measuring the expansion of the universe. The rate of expansion even has a name: "The Hubble Constant". Below is a table summarizing the Hubble constant calculations:
Method
Hubble Constant Value (km/sec/megaparsec)
gravitational lensing
66
Tully-Fisher
61
cepheid distances to galaxies
62
type la supernovae
61
geometric ditance measures
69
The Ever Expanding Universe:
Most recently, analysis of type 1a supernovae data has shown that the expansion of the universe is accelerating. The more the universe expands, the faster it expands. The universe is not only expanding it seems, but expanding forever.