Prospects for constraining the dark energy potential

Abstract

We generalize to non-flat geometries the formalism of Simon et al (2005 Phys. Rev. D 71123001 [astro-ph/0412269]) to reconstruct the dark energy potential. This formalism makes use ofquantities similar to the horizon-flow parameters in inflation, can, in principle, be madenon-parametric and is general enough to be applied outside the simple, single-scalar-fieldquintessence. Since currently available and forthcoming data do not allow a non-parametricand exact reconstruction of the potential, we consider a general parametric description interms of Chebyshev polynomials. We then consider present and future measurements ofH(z), baryon acoustic oscillation (BAO) surveys and supernovae type 1A surveys, and investigatetheir constraints on the dark energy potential. We find that relaxing the flatness assumptionincreases the errors in the reconstructed dark energy evolution but does not open up significantdegeneracies, provided that a modest prior is imposed on the geometry. Direct measurements ofH(z), such as those provided by BAO surveys, are crucially important forconstraining the evolution of the dark energy potential and the dark energyequation of state, especially for non-trivial deviations from the standardΛCDM (CDM: cold dark matter) model.