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 most common measurement is the correlation in alignments of background galaxies which can be used to infer the variance of the projected surface density of matter. This measurement of the fluctuations is insensitive to the total mass content and is analogous to using waves on the ocean to measure its depths. However, when the depth is shallow as happens near a beach waves become skewed. Similarly, a measurement of skewness in the projected matter distribution directly measures the total matter content of the universe. While skewness has already been convincingly detected, its constraint on cosmology is still weak. We address optimal analyses for the CFHT Legacy Survey in the presence of noise. We show that a compensated Gaussian filter with a width of 2.5 arc minutes optimizes the cosmological constraint, yielding m/m 10%. This is significantly better than other filters which have been considered in the literature. This can be further improved with tomography and other sophisticated analyses.

The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of matter in the universe. By comparing predicted strong lensing probabilities with observations, we can test the mass distribution of dark matter halos, in particular, the inner density slope. In this letter, unlike previous work that directly models the density profiles of dark matter halos semi-analytically, we generalize the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White (GNFW) models of three populations with slopes, α, of about -1.5, -1.3 and -1.1 for galaxies, groups and clusters, respectively. This approach is an alternative and independent way to examine the slopes of mass density profiles of halos. We present calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant. It is shown that the compound model of density profiles does not match well with the observed lensing probabilities derived from the Jodrell-Bank VLA Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey data. Together with the previous work on lensing probability, our results suggest that a singular isothermal sphere mass model of less than about 1013h−1M⊙ can predict strong lensing probabilities that are consistent with observations of small splitting angles.

Weak gravitational lensing provides a direct statistical measure of the dark matter distribution. The variance is easiest to measure, which constrains the degenerate product 8 0.6 0. The degeneracy is broken by measuring the skewness arising from the fact that densities must remain positive, which is not possible when the initially symmetric perturbations become non-linear. Skewness measures the non-linear mass scale, which in combination with the variance measures 0 directly. We present the first detection of dark matter skewness from the Virmos-Decart survey. We have measured the full three point function, and its projections onto windowed skewness. We separate the lensing mode and the B mode. The lensing skewness is detected for a compensated Gaussian on scales of 5.37 arc minutes to be k-3=1.06±0.06×10−6. The B-modes are consistent with zero at this scale. The variance for the same window function is k-2=5.32±0.62±0.98×10−5, resulting in S3=375+342−124. Comparing to N-body simulations, we find 0<0.5 at 90% confidence. The Canada-France-Hawaii-Telescope legacy survey and newer simulations should be able to improve significantly on the constraint.

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.