Dark energy parametrizations and the curvature of the universe

We investigate observational constraints on the curvature of the universe not restricting ourselves to a cosmological constant as dark energy, especially allowing a dark energy equation of state to evolve with time in several ways. We use type Ia supernovae (SNeIa) data from the latest gold data set which includes 182 SNeIa, along with the CMB shift parameter and the baryon acoustic oscillation peak. We show quantitatively that the constraint on the curvature of the universe depends on dark energy model: some popular parametrizations give constraints well around flat universe at 5% level (2 sigma C.L.) whereas some parametrizations allow the universe to be as open as Omega_k ~ 0.2.