Dark Energy in a Hyperbolic Universe

Dark energy models due to a slowly evolving scalar (quintessence) field φ are studied for various potentials V (φ) in a universe with negative curvature. The potentials differ in whether they possess a minimum at φ = 0 or are monotonically declining, i. e. have a minimum at infinity. The angular power spectrum Cl of the cosmic microwave background (CMB) as well as the magnitude-redshift relation mB(z) of the type Ia supernovae are compared with the quintessence models. It is demonstrated that some of the models with Ωtot ≃ 0.85 . . .0.9 are in agreement with the observations, i. e. possess acoustic peaks in the angular power spectrum of the CMB anisotropy as observed experimentally, and yield a magnitude-redshift relation in agreement with the data. Furthermore, it is found that the power spectrum P (k) of the large-scale structure (LSS) agrees with the observations too.