Supernova experiments to characterize dark energy require a well designed low redshift program; we consider this for both ongoing/near term (e.g. Supernova Legacy Survey) and comprehensive future (e.g., SNAP) experiments. The derived criteria are: a supernova sample centered near z=0.05 comprising 150-500 (in the former case) and 300-900 (in the latter case) well measured supernovae. Low redshift Type Ia supernovae play two important roles for cosmological use of the supernova distance-redshift relation: as an anchor for the Hubble diagram and as an indicator of possible systematics. An innate degeneracy in cosmological distances implies that 300 nearby supernovae nearly saturate their cosmological leverage for the first use, and their optimum central redshift is z=0.05. This conclusion is strengthened upon including velocity flow and magnitude offset systematics. Limiting cosmological parameter bias due to supernova population drift (evolution) systematics plausibly increases the requirement for the second use to less than about 900 supernovae.

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.

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.

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.