We believe that the universe will expand forever; not only that, but it seems to be speeding up in its expansion rate! How do we know this? Astronomers can measure the spectrum of light from the farthest and brightest objects we can see, supernovas, and can tell that the distance you calculate from their red shifts does not agree with the distance you get just by looking at how bright their light is. So we think they are actually farther away than they appear, which means the universe is expanding at an increasing rate. Eventually everything will just disappear from view!
Another piece of information that astronomers look at is the Cosmic Microwave
Background Radiation (CMBR) - the oldest light we can observe. That tells us that there was a time, about 14 billion years ago, when the universe was like a ball of plasma, like the Sun. We can't observe any electromagnetic radiation from any time before that, because the universe was opaque, like the sun.
What scientists know about the universe stems from Einstein's General Theory of Relativity. Even though the theory is almost 100 years old, there are several possibilities depending on the initial conditions of the actual universe. In particular the total mass and energy content are the parameters that need to be known in order to predict -according to that theory- the subsequent evolution of the universe.
One way scientists work to answer questions like yours is to become acquainted with the theory for some of these possibilities and then see what the universe will look like in each case. Computer simulations have played an important role in this task. The next step is to compare the results of each of these possibilities with what we know about the actual universe from different kinds of observations. One such observation is the way galaxies cluster (form groups) depending on the values of the amount of mass and energy in the universe. According to theory, the result that more closely resembles observations is for a content of mass and energy such that the predicted evolution of the universe is for a never-ending expansion.