Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF) provides a powerful tool to test non-Gaussian features in the convergence field and to discriminate the different cosmological models. In this letter, we present a new PDF space Wiener filter approach to reconstruct the probability density function of the convergence from the noisy convergence field. We find that for parameters comparable to the CFHT legacy survey, the averaged PDF of the convergence in a 3 degree field can be reconstructed with an uncertainty of about 10%, even though the pointwise PDF is noise dominated.

We employ an analytical approach to investigate the signatures of Baryon Acoustic Oscillations(BAOs) on the convergence power spectrum of weak lensing by large scale structure. It is shown that the BAOs wiggles can be found in both of the linear and nonlinear convergence power spectra of weak lensing at about 40≤1≤600, but they are weaker than that of matter power spectrum. Although the statistical error for LSST are greatly smaller than that of CFHT and SNAP survey especially at about 30<1<300, they are still larger than their maximum variations of BAOs wiggles. Thus, the detection of BAOs with the ongoing and upcoming surveys such as LSST, CFHT and SNAP survey confront a technical challenge.

Using the absolute ages of passively evolving galaxies observed at different redshifts, one can obtain the differential ages, the derivative of redshift z with respect to the cosmic time t (i.e. dz/dt). Thus, the Hubble parameter H(z) can be measured through the relation H(z)=−(dz/dt)/(1 + z). By comparing the measured Hubble parameter at different redshifts with the theoretical one containing free cosmological parameters, one can constrain current cosmological models. In this paper, we use this method to present the constraint on a spatially flat Friedmann-Robert-Walker Universe with a matter component and a holographic dark energy component, in which the parameter c plays a significant role in this dark energy model. Firstly we consider three fixed values of c=0.6, 1.0 and 1.4 in the fitting of data. If we set c free, the best fitting values are c=0.26, m0=0.16, h=0.9998. It is shown that the holographic dark energy behaves like a quintom-type at the 1 level. This result is consistent with some other independent cosmological constrains, which imply that c<1.0 is favored. We also test the results derived from the differential ages using another independent method based on the lookback time to galaxy clusters and the age of the universe. It shows that our results are reliable.

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 and reveal different evolutionary properties of the universe. In addition, we combine the observational H(z) data, the cosmic microwave background data and the baryonic acoustic oscillation data to make a joint analysis. We find that 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.

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 z1=0.35 to constrain the Dvali-Gabadadze-Porrati (DGP) universe. For the case with a curvature term, we set a prior h=0.73±0.03 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.