How certain do science believe the universe is expanding? The continue and increased rate of expansion is backed up by red shift, but   that can also be true for a slowing down universe. Can the acceleration of expansion be reducing, still causing red shift since it's accelerating and eventually starts decelerating and for a moment the entire universe stop?
 A: Scientists are fairly certain that the universe expands.

In the famous Hubble diagram you cannot only see that every galaxy or supernova is redshifted ( and therefore moving away from earth with a relative velocity), but that the further away a galaxy is, the more redshifted it is. This means that relative velocities of these galaxies to earth grow with distance. This can have two implications: 
1.: Earth is a unique point in space and EVERY galaxy seems to move away from us. 
2.: We are not special and every galaxy moves away from every other galaxy, meaning that space itself expands. 
In this context, the Hubble diagram can only be explained by accelerated expansion. This observation is backed up by theory. If you look at standard model of cosmology using Friedmann's equations, you can see that in a dark energy dominated universe like ours, you get exponential acceleration for the Robertson-Walker scale factor $a(t)$, which is a measure for the expansion of the universe.
There is no hint in these equations that this acceleration will eventually stop.
A: As to the title: Scientists do not believe. Instead they build and check models, or theories, based on assumptions and using mathematics. The predictions of their model agrees only with observation if the model assumes an expanding universe.
