  The surprising discovery of an accelerating universe led cosmologists to
posit the existence of "dark energy"--a mysterious energy field that permeates
the universe. Understanding dark energy has become the central problem of
modern cosmology. After describing the scientific background in depth, we
formulate the task as a nonlinear inverse problem that expresses the comoving
distance function in terms of the dark-energy equation of state. We present two
classes of methods for making sharp statistical inferences about the equation
of state from observations of Type Ia Supernovae (SNe). First, we derive a
technique for testing hypotheses about the equation of state that requires no
assumptions about its form and can distinguish among competing theories.
Second, we present a framework for computing parametric and nonparametric
estimators of the equation of state, with an associated assessment of
uncertainty. Using our approach, we evaluate the strength of statistical
evidence for various competing models of dark energy. Consistent with current
studies, we find that with the available Type Ia SNe data, it is not possible
to distinguish statistically among popular dark-energy models, and that, in
particular, there is no support in the data for rejecting a cosmological
constant. With much more supernova data likely to be available in coming years
(e.g., from the DOE/NASA Joint Dark Energy Mission), we address the more
interesting question of whether future data sets will have sufficient
resolution to distinguish among competing theories.

Astrophysics