Dark energy in a hyperbolic universe

Dark energy models arising from 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) and the magnitude–redshift relation mB(z) of the type Ia supernovae are compared with those of 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) also agrees with the observations.