Addressing these questions should be done using a tiered approach, with an emphasis on computational work that takes advantage of rapidly developing technologies. Small teams led by individuals are in a good position to push the frontiers of algorithms and new computing architectures. Medium-size groups of several experts are important to make coherent and concerted progress on key numerical issues outlined above. Large, heroic simulations that push the limits of available technology are critical to drive forefront work; these are best facilitated by large computing centers. All of these areas are informed by analytic theory, which is crucial for providing the basic physical underpinnings for more complex models. Together these aspects are fundamentally important for making progress toward understanding the universe, and the galaxies, clusters, black holes, gas, and dark matter within it.
Laboratory astrophysics is clearly important to understanding galaxies, black holes, and clusters across cosmic time. For example, the details of absorption by dust are not understood, even though most cosmic objects are substantially impacted by dust. Similarly, still lacking are important cross sections for hot gas cooler than 4 million degrees, which is significant in clusters and the IGM. Scientists are not sure of recombination rates that determine ionization equilibria. Spectral features at millimeter to infrared wavelengths are especially poorly known and difficult to calculate, as they arise in molecules and clusters of atoms; ALMA will see a forest of lines that, without new laboratory measurements, will be difficult to interpret. Although the lack of laboratory measurements may not today be a limiting factor in the studies outlined earlier in this report, it may well become the limiting factor as the data improve.
We now stand at the threshold of being able to observe the full history of cosmic structure, across all mass scales, from earliest times to the present day. With a judiciously chosen set of new facilities, instruments, and observing strategies, we can learn how galaxies, clusters, and black holes form, evolve, interact, and influence each other, to a degree of accuracy undreamed of just 20 years ago. This unprecedented wealth of data should be accompanied by a concomitant increase in understanding through the development of new analytic and computational theoretical tools. The past decade has brought dramatic advances in cosmology and an emerging picture of the growth of galaxies and black holes across the immensity of cosmic time. The next decade will open up the entire universe to detailed study and will revolutionize our understanding of the processes by which the observable cosmos came to be.