Power of Observational Hubble Parameter Data: a Figure of Merit Exploration

We use simulated Hubble parameter data in the redshift range 0 \leq z \leq 2 to explore the role and power of observational H(z) data in constraining cosmological parameters of the {\Lambda}CDM model. The error model of the simulated data is empirically constructed from available measurements and scales linearly as z increases. By comparing the median figures of merit calculated from simulated datasets with that of current type Ia supernova data, we find that as many as 64 further independent measurements of H(z) are needed to match the parameter constraining power of SNIa. If the error of H(z) could be lowered to 3%, the same number of future measurements would be needed, but then the redshift coverage would only be required to reach z = 1. We also show that accurate measurements of the Hubble constant H_0 can be used as priors to increase the H(z) data's figure of merit.Comment: 8 pages, 1 table, 8 figures. v2: version accepted by Ap

Distinguishing between inhomogeneous model and ΛCDM\Lambda\textrm{CDM} model with the cosmic age method

Cosmological observables could be used to construct cosmological models, however, a fixed number of observables limited on the light cone is not enough to uniquely determine a certain model. A reconstructed spherically symmetric, inhomogeneous model that share the same angular-diameter-distance-redshift relationship $d_A(z)$ and Hubble parameter $H(z)$ besides $\Lambda\textrm{CDM}$ model (which we call LTB-$\Lambda\textrm{CDM}$ model in this paper), may provide another solution. Cosmic age, which is off the light cone, could be employed to distinguish these two models. We derive the formulae for age calculation with origin conditions. From the data given by 9-year WMAP measurement, we compute the likelihood of the parameters in these two models respectively by using the Distance Prior method and do likelihood analysis by generating Monte Carlo Markov Chain for the purpose of breaking the degeneracy of $\Omega_m$ and $H_0$ (the parameters that we use for calculation). The results yield to be: $t_{\Lambda\textrm{CDM}} =13.76 \pm 0.09 ~\rm Gyr$, $t_{\rm {LTB}-\Lambda\textrm{CDM}} =11.38 \pm 0.15 ~\rm Gyr$, both in $1\sigma$ agreement with the constraint of cosmic age given by metal-deficient stars. The cosmic age method that is set in this paper enables us to distinguish between the inhomogeneous model and $\Lambda\textrm{CDM}$ model.Comment: 10 pages, 2 figures, accepted by Physics Letters B. arXiv admin note: text overlap with arXiv:0911.3852 by other author

Statefinder diagnostic for the modified polytropic Cardassian universe

We apply the Statefinder diagnostic to the Modified Polytropic Cardassian Universe in this work. We find that the Statefinder diagnostic is quite effective to distinguish Cardassian models from a series of other cosmological models. The $s-r$ plane is used to classify the Modified Polytropic Cardassian models into six cases. The evolutionary trajectories in the $s-r$ plane for the cases with different $n$ and $\beta$ reveal different evolutionary properties of the universe. In addition, we combine the observational $H(z)$ data, the Cosmic Microwave Background (CMB) data and the Baryonic Acoustic Oscillation (BAO) data to make a joint analysis. We find that \textbf{Case 2} can be excluded at the 68.3% confidence level and any case is consistent with the observations at the 95.4% confidence level.Comment: Comments: Final version for publication in Physical Review D [minor revision to match the appear version] Journal-ref: Physical Review D 75, 083515 (2007

Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data

This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age. Currently, there are two major methods of independent observational H(z) measurement, which we summarize as the "differential age method" and the "radial BAO size method". Starting with fundamental cosmological notions such as the spacetime coordinates in an expanding universe, we present the basic principles behind the two methods. We further review the two methods in greater detail, including the source of errors. We show how the observational H(z) data presents itself as a useful tool in the study of cosmological models and parameter constraint, and we also discuss several issues associated with their applications. Finally, we point the reader to a future prospect of upcoming observation programs that will lead to some major improvements in the quality of observational H(z) data.Comment: 20 pages, 6 figures, and 1 table, uses REVTeX 4.1. Review article, accepted by Advances in Astronom