We investigate how the nature of dark energy affects the determination of the curvature of the universe from recent observations. For this purpose, we consider the constraints on the matter and dark energy density using observations of type Ia supernovae, baryon acoustic oscillation peak and cosmic microwave background with several types of dark energy equation of state. Although it is usually said that the combination of current observations favors a flat universe, we found that a relatively large parameter space allows the universe to be open for a particular model of dark energy. We also discuss what kind of dark energy model or prior allow a non-flat universe.
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