Arguably two of the greatest theories in physics were developed in the last century: General relativity and Quantum Field theory. While the former only really affects results at very large scales, the latter describes interactions at very small scales (or very high energies). Our daily experiences are stuck somewhere in between so we don't really see either and still stick to what Sir Newton came up with in the 17th century. Of course, both theories will apply all the time but as a general rule, it is easy for physicists to decide which one is important and which one is not for the problem they are looking it.
If we look at the whole universe today, it is very large and, on average, very cold. Therefore, it is easy to conclude that one has to look to general relativity to figure out how things work. There is a problem though: The universe is also rather complicated. There are galaxies, and nebula and black holes and all sorts of other stuff. If one really wanted to solve the equation of general relativity, one would have to take every star, every gas cloud and every stray planet into account. That's just not possible, there is no computer anywhere near strong enough to do that, and to be honest, we don't even know where everything is. So what do physicists do in a situation like that? We approximate. In this case, we assume that the universe looks the same anywhere and in any direction (this is called the cosmological principle, by the way). Basically, what we are saying is that we are pretending that all the matter and energy in the universe is collected, ground to dust and distributed evenly everywhere ( and for us physicists, matter and energy are pretty much the same thing, apart from a few factors of the speed of light. Hello E=mc2 ). Now, of course we know that's not true. Matter and energy come in lumps. Being on earth is very different to floating out in space. The Milky Way looks very different to "empty" space out somewhere far away from any galaxy. But the universe is a very large space and if we zoom out far enough, the cosmological principle is a pretty good approximation. Saying that it looks the same in every direction is just us saying that we are not in a special place ie not at the centre of the universe. General Relativity + the Cosmological Principle = Cosmology.
Cosmology has done a pretty good job at explaining quite a few things we observe, for example the ratio of light elements (such as Hydrogen and Helium) in the universe. Or why stars that are further away look redder than ones that are much closer to us. But there are also quite a few problem which Cosmology currently cannot explain and I am working on one of them: The flatness problem. Much like a surface, three dimensional space can be curved. For a surface, the three configurations are very easy to see: Flat, closed and open. Unfortunately, our brains is apparently not really equipped to imagine 3-D space curving (mine definitely isn't, maybe yours is) but from the way light travels to us from very far away, we can tell that our universe is almost or completely flat. This is a little puzzling as all our theories in cosmology suggest that if it is even a tiny bit curved, it should become more and more curved over time. The universe is about 14 billion years old so one would think it has had plenty of time to sort itself out. As an analogy, it is as if Sir Newton derived the law of gravity and found that it makes everything into spheres ( which it does ), only to then measure that our earth appears to be a disc anyway. It is possible the the universe is almost flat today, but this would have required the universe to be even flatter in the beginning. Basically, it would have required our universe to start of in a very special condition indeed and so far, we have no good mechanism to explain why it would start of in exactly this setup.
But then, this brings us to another problem in Cosmology: We don't know very much about the early universe at all anyway. And in fact we now believe that our current theories don't even apply. As I said before, general relativity is great for big scales but as we go back in time, everything becomes smaller and smaller and smaller which in this case also means hotter and hotter and hotter. At very high temperatures, quantum effects should take over and classical cosmology does not take this into account at all. One attempt at introducing quantum effects where appropriate is called quantum gravity ( another attempt at solving this dilemma is string theory ). Quantum gravity is great but, much like general relativity, much to complicated to actually work with. So, just like before, we make the same assumptions: The universe looks the same everywhere and in every direction. The result is called quantum cosmology and this finally brings us to the theory I work with: Loop Quantum Cosmology, a subset again. I'm not even going to attempt to explain the loops part, its really just due to the mathematical technique involved.
So, all of this was rather long and complicated. What am I actually doing? I try to answer the question why the geometry of the universe looks the
way it does today, even though our classical equations suggest it
should not look like this for very long. I am hoping that the answer is
"Quantum effects in the very early universe", which might then have set
up the univese just right to come out as we see it today. For this, I use a theory called Loop Quantum Cosmology, which is an attempt at merging general relativity with quantum field theory to accurately describe the very early universe.
Well done if you actually read all of this. I'd be very happy to answer any question. :)