It's possible to learn about conditions in the very early Universe through a variety of methods. Underlying everything is the idea that the Universe we see today originated in a tiny region, and has since expanded. These days there's so much evidence for such a claim that it's taken as a simple fact.
The early Universe
Projects like CERN's Large Hadron Collider aim to uncover aspects of the evolution of the Universe. By smashing particles together at extremely high speed, they probe physics at very high energy. But unfortunately they get nowhere near the energy involved in modern cosmology. The LHC is typically dealing with energies of up to around 10 TeV (TeV being a measure of energy). The Planck scale, the representative energy of the ‘big bang’ itself, is about a million billion times larger than that. The LHC is filling in details about how the Universe cooled down, long after the really exciting stuff happened!
The leading theory about the very early Universe today is inflation. The idea is that the Universe underwent a short period of exponential expansion at energies somewhat lower than the Planck scale (but still enormously higher than the LHC scale).
If inflation is right, the universe at early times was filled not with matter and radiation as it is today, but with a much more exotic source of energy. It would therefore have expanded at a different rate from that expected if normal matter were present.
One way of thinking about inflation is that it predicts a slower rate of expansion in the very early Universe compared to that extrapolated from the behaviour of the Universe today. This makes the Universe a fraction older than it would be according to non-inflating models, which gives a bit of time to (at least potentially) iron out some problematic lumps and bumps which might otherwise be present immediately after the big bang.
It might all sound a bit vague — in fact inflation's precise motivations have been debated widely. Whether inflation is really a satisfactory way to iron out unsavoury features of the normal big bang picture remains under question. (Prominent scientists who have expressed their doubts include Roger Penrose and Sean Carroll.)
It would be fair to say that inflation is not a complete picture, or at least not a completely understood one. But it is the most widely accepted of the speculative early-Universe theories. And it does lead to specific predictions about how the Universe should be organized on large scales. Right now, it seems that many of those predictions have been confirmed by observations like those of WMAP.
On a broad level, my own work in this area can therefore be seen as trying to understand how we can rigorously put inflationary theory to the test. In the presence of severe limiting factors like cosmic variance, that task challenges not only our understanding of physics, but also of statistics!
I'm interested in these kind of statistical challenges and also in how general relativity, Einstein's theory of gravity, helps us understand the early Universe and the predictions it makes for the cosmic microwave background. For more information, see my publications page.