Dark energy in a hyperbolic universe

Dark energy models arising from a slowly evolving scalar (quintessence) field Phi are studied for various potentials V (Phi ) in a universe with negative curvature. The potentials differ in whether they possess a minimum at Phi =0 or are monotonically declining, i.e. have a minimum at infinity. The angular power spectrum C (l) of the cosmic microwave background (CMB) and the magnitude-redshift relation m (B) (z ) of the type Ia supernovae are compared with those of the quintessence models. It is demonstrated that some of the models with Omega(tot) similar or equal to0.85-0.9 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) also agrees with the observations.