Unlike most computational problems in many areas of science, the cosmological problem is blessed with known, well-specified initial conditions. Within a general class of models, it is possible to calculate the properties of primordial perturbations in the cosmic energy density generated by quantum processes during an early inflationary epoch. In a wide family of inflationary models, these perturbations are adiabatic, scale-invariant and have Gaussian-distributed Fourier amplitudes. The model also requires an assumption about the nature of the dark matter and the possibilities have now been narrowed down to non-baryonic candidates of which cold dark matter particles seem the most promising. An empirical test of the initial conditions for the formation of structure predicted by the model is provided by the cosmic microwave background radiation. The tiny temperature fluctuations it exhibits have exactly the properties expected in the model. Furthermore, the CMB data can be used to fix some of the key model parameters such as and b, while these data, combined with other recent datasets such as the 2dFGRS, allow the determination of many of the remaining parameters such as , and h. It this specificity of the cosmological problem that has turned simulations into the primary tool for connecting cosmological theory to astronomical observations.
In addition to well-specified initial conditions, the cosmological dark matter problem has the advantage that the only physical interaction that is important is gravity. The problem can thus be posed as a gravitational N-body problem and approached using the many sophisticated techniques that have been developed over the past two decades to tackle this problem. Although on small scales there remain a number of unresolved issues, it is fair to say that on scales larger than a few megaparsecs, the distribution of dark matter in CDM models is essentially understood. The inner structure of dark matter halos, on the other hand, is still a matter of debate and the mass function of dark matter halos has only been reliably established by simulations down to masses of order 1011 M. Resolving these outstanding issues is certainly within reach, but this will require carefully designed simulations and large amounts of computing power.
The frontier of the subject at present lies in simulations of the formation, evolution and structure of galaxies. This problem requires first of all a treatment of gas dynamics in a cosmological context and a number of techniques, relying on direct simulations or on semi-analytical approximations, are being explored. There are quite a few different approaches to cosmological gasdynamics, but it is reassuring that they all give similar results in the simplest relevant problem, the evolution of non-radiative gas during the formation of a galaxy cluster. No detailed comparisons exist yet for the more complicated case in which the gas is allowed to cool, but at least one of the gasdynamic simulation techniques, SPH, gives quite similar results to a simple semi-analytic approach. Realistic models of galaxy formation, however, will require much more than a correct treatment of cooling gas. Such models will necessarily have to include a plethora of astrophysical phenomena such as star formation, feedback, metal enrichment, etc. The huge disparity between the submegaparsec scales on which these processes operate and the gigaparsec scale of the large-scale structure makes it impossible to contemplate a comprehensive ab initio calculation. The way forward is clearly through a hybrid approach combining direct simulation of processes operating on a limited range of scales with a phenomenological treatment of the others. There is currently a great deal of activity in the phenomenology of galaxy formation.
In spite of the uncertainties that remain, all the indications are that our Universe is well described by a model in which
A skeptic is entitled to feel that the current paradigm is odd, to say the least. Not only is there a need to invoke vast amounts of as yet undetected non-baryonic cold dark matter, but there is also the need to account for the dominant presence of a dark energy whose very existence is a mystery within conventional models of fundamental physics. Odd as it may seem, however, this model accounts remarkably well for a large and diverse collection of empirical facts that span 13 billion years of evolution.
I am grateful to my collaborators for their contribution to the work reviewed here, especially Carlton Baugh, Andrew Benson, Shaun Cole, Adrian Jenkins, Cedric Lacey, Peder Norberg, John Peacock, Will Percival, and Simon White.