On the determination of curvature and dynamical dark energy

Constraining simultaneously the dark energy (DE) equation of state and the curvature of the universe is difficult due to strong degeneracies. To circumvent this problem when analyzing data it is usual to assume flatness to constrain the DE or, conversely, to assume that the DE is a cosmological constant to constrain the curvature. In this paper, we quantify the impact of such assumptions with an eye to future large surveys. We simulate future data for type Ia supernovae, the cosmic microwave background and baryon acoustic oscillations for a large range of fiducial cosmologies allowing a small spatial curvature. We take into account a possible time evolution of DE through a parameterized equation of state: w(a) = w(0)+(1-a)w(a). We then fit the simulated data with a wrong assumption on the curvature or on the DE parameters. For a fiducial CDM cosmology, if flatness is incorrectly assumed in the fit and if the true curvature is within the ranges 0.01 < Omega(k) < 0.03 and -0.07 < Omega(k) < -0.01, one will be led to conclude erroneously that an evolving DE is present, even with high statistics. On the other hand, models with curvature and dynamical DE can be confused with a. at flat Lambda CDM model when the fit ignores a possible DE evolution. We find that, in the future, with high statistics, such risks of confusion should be limited, but they are still possible, and biases in the cosmological parameters might be important. We conclude by recalling that, in the future, it will be mandatory to perform some complete multi-probe analyses, leaving the DE parameters as well as the curvature as free parameters.