Cosmological Inflation is an addition to the highly successful "big bang" model of the universe. Looking backwards in time, the big bang model says that the universe becomes radiation-dominated and that the density/temperature increase unboundedly in finite time, leading to the big bang. Inflation rather says that it is not radiation "all the way back" but that the radiation emerges out of a preceding "inflating" phase.
During this phase the matter content of the universe is dominated by a hypothetical "scalar field" form of matter called the "inflaton". The universe expands in an accelerated manner as the inflaton relaxes from a higher value to a lower one, with the acceleration decreasing as the field drops. Eventually inflation ends and the inflaton decays into "regular" radiation leading into an apparently usual big bang. Whether there is a singularity or anything else before inflation is a matter under academic discussion. The inflating phase allows for at least a tiny fraction more time in the early universe and potentially enough time to address some of the puzzles of the pure big bang model, in particular its horizon problem (the lack of a causal mechanism to explain observed large-separation correlations in the universe). A big success for inflation then came in that it was realized that small quantum fluctuations of the scalar field during inflation could plausibly seed the structure that we see has since developed in our universe. For this to work there has to have been an expansion of at least e^~60 in the size of the universe during inflation.
However, the quantum fluctuations necessary to explain structure do not act solely at lowish inflaton field values. They act at higher field values as well, and in the so-called "large field" models that I'm focusing on here the fluctuations' strength grows as the field value increases. So the fluctuations should be taken into account for the entire history of the field, and then it seems that "eternal inflation" may occur. Here a runaway situation occurs with regions that fluctuate uphill inflating faster, allowing growing physical volumes of space to sustain inflation forever. We would live in a rare region where inflation ends. However, then it is not clear that the most likely end-path is the "classical" one mentioned above that gives inflation its predictive successes; instead the field might "on average" jump down from high values at the last possible moment, leading to Guth's "Youngness Paradox". This paradox asks why the universe appears to be so old when it would have been favourable because of the vastly larger volume generated for it to have inflated until the last possible moment consistent with the formation of life.
In our 2005 hep-th paper, Neil Turok and I introduced a nice framework in which to study eternal inflation. We realized that for a quartic potential in a flat potential, the Hubble radius turns out to follow a simple linear Langevin equation. Thus we could perturbatively investigate the behaviour of the system, and found that something like eternal inflation only occurred with a non-local final-volume weighting. We also looked at how the Hubble radius would behave, without weightings, under a constraint on initial and final states. Using such paths is probably the only way to investigate past histories of regions where inflation has come to an end. Unfortunately, such paths are an exponentially tiny subset of the (simulable) unconstrained ones and so a numerical simulation in the constrained case has seemed totally hopeless.
Now I have some new ideas on perturbatively weighting constrained paths and on how to numerically simulate them too. Thus I am working on generating many constrained paths and non-perturbatively weighting them. This should enable an investigation of the youngness paradox and, more generally, the effect of initial conditions on late-time behaviour. This is an ideal problem for GPGPU and hence my interest in using graphics card computing for cosmology.
See the progress page for details of how I am getting on.