Dark Energy in a Hyperbolic Universe

Dark energy models due to 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 monotonously declining, i.e. have a minimum at infinity. The angular power spectrum C_l of the cosmic microwave background (CMB) as well as the magnitude-redshift relation m_B(z) of the type Ia supernovae are compared with the quintessence models. It is demonstrated that some of the models with $\Omega_{tot} \simeq 0.85...0.9$ are in agreement with the observations, i.e. possess a first acoustic peak in the CMB anisotropy at $l\simeq 210...220$ and yield a magnitude-redshift relation in agreement with the observations. Furthermore, it is found that the power spectrum $P(k)$ of the large-scale structure is in agreement with the observations too, with a bias parameter $b \simeq 1.1$.