  Many of the most exciting questions in astrophysics and cosmology, including
the majority of observational probes of dark energy, rely on an understanding
of the nonlinear regime of structure formation. In order to fully exploit the
information available from this regime and to extract cosmological constraints,
accurate theoretical predictions are needed. Currently such predictions can
only be obtained from costly, precision numerical simulations. This paper is
the third in a series aimed at constructing an accurate calibration of the
nonlinear mass power spectrum on Mpc scales for a wide range of currently
viable cosmological models, including dark energy. The first two papers
addressed the numerical challenges, and the scheme by which an interpolator was
built from a carefully chosen set of cosmological models. In this paper we
introduce the "Coyote Univers"' simulation suite which comprises nearly 1,000
N-body simulations at different force and mass resolutions, spanning 38 wCDM
cosmologies. This large simulation suite enables us to construct a prediction
scheme, or emulator, for the nonlinear matter power spectrum accurate at the
percent level out to k~1 h/Mpc. We describe the construction of the emulator,
explain the tests performed to ensure its accuracy, and discuss how the central
ideas may be extended to a wider range of cosmological models and applications.
A power spectrum emulator code is released publicly as part of this paper.
