uncertainties from varied combinations of data sets. To exploit these advances requires both cutting-edge computer hardware and the software, personnel support, and the training of researchers needed to maximize its scientific reach. This support is needed at many levels, from the handful of ultrapowerful machines that enable the most ambitious calculations, through the larger and more varied tier of supercomputers available at national and state-supported centers, and on to high-performance clusters in individual research groups and the networks of workstations and laptops by which scientists access these facilities and examine the results of their computations.

Although the advances in computational theory are dramatic, it is often penciland-paper theory that leads to novel ideas or identifies the connections between seemingly disparate phenomena. The frontiers of cosmology today present grand theoretical challenges: rooting models of inflation in more fundamental descriptions of underlying physics; explaining the asymmetry between matter and antimatter and thus the origin of the particles that form Earth and the life on its surface; describing the interior structure of black holes and explaining their entropy in terms of quantum gravity; determining whether there are spatial dimensions beyond the three of everyday experience; explaining the surprising magnitude of cosmic acceleration and the seeming coincidence of the densities of baryons, dark matter, and dark energy; and determining whether our observable cosmos is a fully representative sample of the universe or one of many disparate bubbles in a much larger inflationary sea. Robust support for the full span of theoretical activities is essential in order to reap the return from large investments in observational facilities over the next decade, and also to ensure that the scientific opportunities in the 2020-2030 decade will be as exciting as those of today.

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