Prospects in Constraining the Dark Energy Potential
  We generalize to non-flat geometries the formalism of Simon et al. (2005) to reconstruct the dark energy potential. This formalism makes use of quantities similar to the Horizon-flow parameters in inflation, can, in principle, be made non-parametric and is general enough to be applied outside the simple, single scalar field quintessence. Since presently available and forthcoming data do not allow a non-parametric and exact reconstruction of the potential, we consider a general parametric description in term of Chebyshev polynomials. We then consider present and future measurements of H(z), Baryon Acoustic Oscillations surveys and Supernovae type 1A surveys, and investigate their constraints on the dark energy potential. We find that, relaxing the flatness assumption increases the errors on the reconstructed dark energy evolution but does not open up significant degeneracies, provided that a modest prior on geometry is imposed. Direct measurements of H(z), such as those provided by BAO surveys, are crucially important to constrain the evolution of the dark energy potential and the dark energy equation of state, especially for non-trivial deviations from the standard LambdaCDM model. 
Enrique Fernandez-Martinez and Licia Verde