  We discuss the cosmological degeneracy between the Hubble parameter H(z), the
age of the universe and cosmological parameters describing simple variations
from the minimal LCDM model. We show that independent determinations of the
Hubble parameter H(z) such as those recently provided by Simon et al., Phys.
Rev. D 71 (2005) 123001, combined with Cosmic Microwave Background data, can
provide stringent constraints on possible deviations from the LCDM model. In
particular we find that this data combination constrains at the 68% (95%)
confidence level the following parameters: sum of the neutrino masses < 0.5
(1.0) eV, number of relativistic neutrino species N_rel = 4.1^{+0.4}_{-0.9}
(^{+1.1}_{-1.5}), dark energy equation of state parameter w = -0.95 +- 0.17 (+-
0.32), and curvature \Omega_k = 0.002 +- 0.006 (+- 0.014), in excellent
agreement with dataset combinations involving Cosmic Microwave Background,
Supernovae and Baryon Acoustic Oscillations. This offers a valuable consistency
check for systematic errors.
