For exploring the physics behind the accelerating universe a crucial question is how much we can learn about the dynamics through next generation cosmological experiments. For example, in defining the dark energy behavior through an effective equation of state, how many parameters can we realistically expect to tightly constrain? Through both general and specific examples (including new parametrizations and principal component analysis) we argue that the answer is 42 - no, wait, two. Cosmological parameter analyses involving a measure of the equation of state value at some epoch (e.g., w_0) and a measure of the change in equation of state (e.g., w') are therefore realistic in projecting dark energy parameter constraints. More elaborate parametrizations could have some uses (e.g., testing for bias or comparison with model features), but do not lead to accurately measured dark energy parameters.

The accelerating expansion of the universe presents an exciting, fundamental challenge to the standard models of particle physics and cosmology. I highlight some of the outstanding challenges in both developing theoretical models and interpreting without bias the observational results from precision cosmology experiments in the next decade that will return data to help reveal the nature of the new physics. Examples given focus on distinguishing a new component of energy from a new law of gravity, and the effect of early dark energy on baryon acoustic oscillations.

In the quest for precision cosmology, one must ensure that the cosmology is accurate as well. We discuss figures of merit for determining from observations whether the dark energy is a cosmological constant or dynamical, with special attention to the best determined equation of state value, at the ``pivot'' or decorrelation redshift. We show this is not necessarily the best lever on testing consistency with the cosmological constant, and moreover is subject to bias. The standard parametrization of w(a)=w_0+w_a(1-a) by contrast is quite robust, as tested by extensions to higher order parametrizations and modified gravity. Combination of complementary probes gives strong immunization against inaccurate, but precise, cosmology.

A single parameter, the gravitational growth index gamma, succeeds in characterizing the growth of density perturbations in the linear regime separately from the effects of the cosmic expansion. The parameter is restricted to a very narrow range for models of dark energy obeying the laws of general relativity but can take on distinctly different values in models of beyond-Einstein gravity. Motivated by the parameterized post-Newtonian (PPN) formalism for testing gravity, we analytically derive and extend the gravitational growth index, or Minimal Modified Gravity, approach to parameterizing beyond-Einstein cosmology. The analytic formalism demonstrates how to apply the growth index parameter to early dark energy, time-varying gravity, DGP braneworld gravity, and some scalar-tensor gravity.

Non-negligible dark energy density at high redshifts would indicate dark energy physics distinct from a cosmological constant or "reasonable'" canonical scalar fields. Such dark energy can be constrained tightly through investigation of the growth of structure, with limits of > 1 for many models. Intermediate dark energy can have effects distinct from its energy density; the dark ages acceleration can be constrained to last less than 5percent of a Hubble e-fold time, exacerbating the coincidence problem. Both the total linear growth, or equivalently sigma 8, and the shape and evolution of the nonlinear mass power spectrum for z<2 (using the Linder-White nonlinear mapping prescription) provide important windows. Probes of growth, such as weak gravitational lensing, can interact with supernovae and CMB distance measurements to scan dark energy behavior over the entire range z=0-1100.

X-ray cluster measurements interpreted with a universal baryon/gas mass fraction can theoretically serve as a cosmological distance probe. We examine issues of cosmological sensitivity for current (e.g., Chandra X-ray Observatory, XMM-Newton) and next generation (e.g., Con-X, XEUS) observations, along with systematic uncertainties and biases. To give competitive next generation constraints on dark energy, we find that systematics will need to be controlled to better than 1percent and any evolution in f_gas (and other cluster gas properties) must be calibrated so the residual uncertainty is weaker than (1+z)0.03.

The cosmic expansion history tests the dynamics of the global evolution of the universe and its energy density contents, while the cosmic growth history tests the evolution of the inhomogeneous part of the energy density. Precision comparison of the two histories can distinguish the nature of the physics responsible for the accelerating cosmic expansion: an additional smooth component - dark energy - or a modification of the gravitational field equations. With the aid of a new fitting formula for linear perturbation growth accurate to 0.05-0.2percent, we separate out the growth dependence on the expansion history and introduce a new growth index parameter \gamma that quantifies the gravitational modification.