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.

It has been revealed recently that, in the scale free range, i.e. from the scale of the onset of nonlinear evolution to the scale of dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the self-similar log-Poisson hierarchy. As a consequence of this evolution, the relations among various physical quantities of cosmic baryon fluid should be scale invariant, if the physical quantities are measured in cells on scales larger than the dissipation scale, regardless the baryon fluid is in virialized dark halo, or in pre-virialized state. We examine this property with the relation between the Compton parameter of the thermal Sunyaev-Zel'dovich effect, y(r), and X-ray luminosity, Lx(r), where r being the scale of regions in which y and Lx are measured. According to the self-similar hierarchical scenario of nonlinear evolution, one should expect that 1.) in the y(r)-Lx(r) relation, y(r)=10A(r)[Lx(r)](r), the coefficients A(r) and (r) are scale-invariant; 2.) The relation y(r)=10A(r)[Lx(r)] (r) given by cells containing collapsed objects is also available for cells without collapsed objects, only if r is larger than the dissipation scale. These two predictions are well established with a scale decomposition analysis of observed data, and a comparison of observed y(r)-Lx(r) relation with hydrodynamic simulation samples. The implication of this result on the characteristic scales of non-gravitational heating is also addressed.

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.

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.