Mapping the cosmological expansion is a key endeavour in our quest for understanding physics - gravitation and other forces, spacetime, the vacuum - and the origin, evolution, and future of the universe. The Big Bang model of a hot, dense, early universe expanding and adiabatically cooling, and forming structure through gravitational instability from primordial seed perturbations, is remarkably successful and simple. The concordance cosmology is (close to) spatially flat and 13.7 billion years old. This clear statement represents a substantial advance of our knowledge over a decade ago.
The discovery of the acceleration of the cosmic expansion created a renaissance of cosmological exploration, offering the hope of connecting quantum physics and gravitation, extra dimensions and the nature of spacetime, while severing the bonds between geometry and destiny. This opens up completely two premier questions in science: the origin and the fate of the universe. To understand the nature of the gravitationally repulsive dark energy pulling the universe apart, we must map the cosmological expansion in greater detail and accuracy than ever envisioned.
We have shown that a considerable part of the optimal approach for mapping the expansion history is set purely by the innate cosmological dependences. Observational programs must follow these foundations as basic science requirements: in particular the need for a wide range of redshifts, z 0-2 and robust anchoring to either low or high redshift. Our capabilities for measuring the expansion through direct geometric probes are increasing, and techniques are continuing to develop. There are no short cuts - detailed design of successful surveys works within this framework with the purpose to minimize systematic uncertainties in the measurements.
Every technique has systematic uncertainties, appearing in multiple guises. While observational systematics are most familiar, arising even in purely geometric techniques, equally important are issues in the data analysis, e.g. combining heterogeneous data sets, and in the theoretical interpretation, e.g. susceptibility to biases from assumptions of high redshift behavior or of non-expansion physics (perturbation growth behavior, coupling, etc.).
We have given several concrete examples of the effects of systematic uncertainties for various probes. These provide a cautionary tale for survey design, as we are now entered into the systematics dominated data era - and may well soon approach the theory systematics era. We cannot rely on assumptions that any part of the dark sector is simple and ignorable while we concentrate on another aspect. For true progress, we emphasized the role of complementarity in building from robust, clean answers to more complex investigations. Probes employing growth of structure give windows on both expansion per se and gravitational laws, and we commented that the excitement of testing general relativity is equally matched with the challenge of creating a framework for analysis.
Acceleration of the cosmic expansion heralds a revolution in physics, if we can characterize and understand it. To comprehend this new aspect of the universe, we must map the expansion not only at recent epochs, but encompass the early universe. Once we have garnered sufficient understanding, the prize is answering the question of the fate of the universe, now unbound from the question of the cosmic geometry. The good news is that we likely have at least 24 billion years to do so!
I thank the Aspen Center for Physics for a superb working environment, and Los Alamos National Laboratory and the Santa Fe 07 workshop, University of Heidelberg, and the Dark Cosmology Centre and Niels Bohr Summer Institute, for hospitality. I gratefully acknowledge contributions by Georg Robbers, Ramon Miquel, and David Rubin of Figures 11, 18, and 19 respectively. Colleagues too numerous to mention helped form my thinking on this wide ranging topic, but I will single out Bob Wagoner for laying the foundations. This work has been supported in part by the Director, Office of Science, Department of Energy under grant DE-AC02-05CH11231.