In this paper, we use a set of observational $H(z)$ data (OHD) to constrain the $Lambda$CDM cosmology. This data set can be derived from the differential ages of the passively evolving galaxies. Meanwhile, the $mathcal {A}$-parameter, which describes
the Baryonic Acoustic Oscillation (BAO) peak, and the newly measured value of the Cosmic Microwave Background (CMB) shift parameter $mathcal {R}$ are used to present combinational constraints on the same cosmology. The combinational constraints favor an accelerating flat universe while the flat $Lambda$CDM cosmology is also analyzed in the same way. We obtain a result compatible with that by many other independent cosmological observations. We find that the observational $H(z)$ data set is a complementarity to other cosmological probes.
The thermodynamical properties of dark energy are usually investigated with the equation of state $omega =omega_{0}+omega_{1}z$. Recent observations show that our universe is accelerating, and the apparent horizon and the event horizon vary with reds
hift $z$. When definitions of the temperature and entropy of a black hole are used to the two horizons of the universe, we examine the thermodynamical properties of the universe which is enveloped by the apparent horizon and the event horizon respectively. We show that the first and the second laws of thermodynamics inside the apparent horizon in any redshift are satisfied, while they are broken down inside the event horizon in some redshift. Therefore, the apparent horizon for the universe may be the boundary of thermodynamical equilibrium for the universe like the event horizon for a black hole.
In this work, we use observations of the Hubble parameter from the differential ages of passively evolving galaxies and the recent detection of the Baryon Acoustic Oscillations (BAO) at $z_1=0.35$ to constrain the Dvali-Gabadadze-Porrati (DGP) univer
se. For the case with a curvature term, we set a prior $h=0.73pm0.03$ and the best-fit values suggest a spatially closed Universe. For a flat Universe, we set $h$ free and we get consistent results with other recent analyses.
