# Measuring the Fate of the Universe

As the Universe expands, gravity pulls on the Universe, and slows the expansion down over time. As we look to great distances, we are looking back in time. If we can measure how fast the Universe is expanding in the past, and compare it to how fast it is expanding now, we can see the total gravitational effect of all matter in the Universe.

Here we plot the distance between two galaxies as a function of time. Looking back into the past we see that the galaxies get closer together until they are ontop of each other - this is the time of the Big Bang. If the Universe expands at the same rate, it will follow the dotted yellow path. But if it is slowing down over time the Universe is younger than we would otherwise think, speeding up, then it is older.

If there is lots of material, the Universe will be expanding much faster in the past --- it will have slowed down a lot --- so much so that the Universe will eventually halt in its expansion, start to contract, and eventually end in the gnaB giB (that is the Big Bang backwards). In most models of the universe, this type of Universe curves onto itself (like a sphere), and is finite.

If there isn't much material, the Universe will be expanding about the same speed in the past as now, and will continue to expand forever. This type of universe curves away from itself (like a saddle), and therefore is without end, now, in the future, and even at the time of the Big Bang.

Here we once again plot the distance between two galaxies as a function of time. Looking into the future we see that the galaxies get further and further apart, except if gravity is able to halt the expansion. If the Universe expands at the same rate, it will follow the dotted yellow path. But if it is slowing down over time the Universe it eventually turns around and starts to contract. If the Universe is speeding up, it will continue to do so at an ever increasing rate.

A favourite model amongst theorists is for the Universe to be precariously balanced between being finite and infinite. This balanced Universe is known as a critical universe. Space neither curves away nor onto itself, it is flat, and is, for most theorists infinite. A final possibility is that the Universe has something other than gravity in it which accelerates the Universe over time. It would be a mysterious substance indeed which did this!

2D representations of the shape of the Universe. Universes with lots of material curve onto themselves like a sphere. Universes with little matter curve away from themselves like a saddle. And Universes with just the right amount of material are flat.

We use Einstein's equations of General Relativity to understand what we see in the Universe. In addition to assuming his theory is right (it sure seems to be everywhere we have be able to measure so far), we do have to make a few assumptions. The most important of these are that the universe is homogenous (that is, the material in the Universe is, on average, evenly spread through out the Universe) and isotropic (matter, the expansion, and everything else is the same in all directions that we look). With these assumptions we can predict how bright an object will be given its rate of recession (the simple relation found by Hubble breaks down at large distances).

If we can measure distances, we can see how these compare to the predictions of General Relativity, and in this way we can see what is in the Universe, and gauge how this material affects the Universe. It turns out this also allows us to predict what the future holds for the Universe.

But to do this we need a way of measuring distances halfway across the visible Universe. Measuring distances in astronomy is not trivial and this process has lead to some of the greatest controversies in astronomy over the past two hundred years. Galaxies, which are bright enough to be seen to the great distances required, unfortunately, seem to evolve over time, so comparing the size or brightness of galaxies we see today to those in the distant Universe is fraught with danger. However, Type Ia supernovae, which are individual stars, can also be seen to these great distances, and these are what we have use to measure the Universe.