QSO lensing magnification associated with galaxy groups

We simulated both the matter and light (galaxy) distributions in a wedge of the Universe and calculated the gravitational lensing magnification caused by the mass along the line-of-sight of galaxies and galaxy groups identified in sky surveys. A large volume redshift cone containing cold dark matter particles mimics the expected cosmological matter distribution in a flat universe with low matter density and a cosmological constant. We generate a mock galaxy catalogue from the matter distribution and identify thousands of galaxy groups in the luminous sky projection. We calculate the expected magnification around galaxies and galaxy groups and then the induced quasi-stellar object (QSO)–lens angular correlation due to magnification bias. This correlation is observable and can be used both to estimate the average mass of the lens population and to make cosmological inferences. We also use analytical calculations and various analyses to compare the observational results with theoretical expectations for the cross-correlation between faint QSOs from the 2dF Survey and nearby galaxies and groups from the Automated Plate Measurement and Sloan Digital Sky Survey Early Data Release. The observed QSO–lens anticorrelations are stronger than the predictions for the cosmological model used. This suggests that there could be unknown systematic errors in the observations and data reduction, or that the model used is not adequate. If the observed signal is assumed to be solely due to gravitational lensing, then the lensing is stronger than expected, due to more massive galactic structures or more efficient lensing than simulated.     

Weak lensing of the CMB: extraction of lensing information from the trispectrum

We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities.     

Weak lensing of the CMB by large-scale structure

Several recent papers have studied lensing of the CMB by large-scale structures, which probes the projected matter distribution from z=10³ to z0. This interest is motivated in part by upcoming high resolution, high sensitivity CMB experiments, such as APEX/SZ, ACT, SPT or Planck, which should be sensitive to lensing. In this paper, we examine the reconstruction of the large-scale dark matter distribution from lensed CMB temperature anisotropies. We go beyond previous work in using numerical simulations to include higher order, non-Gaussian effects and find that the convergence and its power spectrum are biased, with the bias increasing with the angular resolution. We also study the contamination by the kinetic Sunyaev–Zel'dovich signal, which is spectrally indistinguishable from lensed CMB anisotropies, and find that it leads to an overestimate of the convergence. We finish by estimating the sensitivity of the previously cited experiments and find that all of them could detect the lensing effect, but would be biased at around the 10% level.     

Investigating cosmological weak lensing with the ray-bundle method

Using the ray-bundle method for calculating gravitational lens magnifications, we outline a method by which the magnification probability may be determined specifically in the weak lensing limit for cosmological models obtained from N -body simulations.
16 different models are investigated, which are variations on three broad classes of cold dark matter model: the standard model with  (Ω₀, λ ₀)=(1.0,0.0)  , the open model with  (Ω₀, λ ₀)=(0.3,0.0)  and the lambda model, which is a flat model with a cosmological constant  (Ω₀, λ ₀)=(0.3,0.7)  .
The effects of varying the Hubble parameter, H ₀, the power spectrum shape parameter, Γ, and the cluster mass normalization, σ ₈, are studied. It is shown that there is no signature of these parameters in the weak lensing magnification distributions. The magnification probability distributions are also shown to be independent of the numerical parameters such as the lens mass and simulation box size in the N -body simulations.     

Weak lensing in the second post-Newtonian approximation: gravitomagnetic potentials and the integrated Sachs–Wolfe effect

Dark matter currents in the large-scale structure give rise to gravitomagnetic terms in the metric, which affect the light propagation. Corrections to the weak-lensing power spectrum due to these gravitomagnetic potentials are evaluated by perturbation theory. A connection between gravitomagnetic lensing and the integrated Sachs–Wolfe (iSW) effect is drawn, which can be described by a line-of-sight integration over the divergence of the gravitomagnetic vector potential. This allows the power spectrum of the iSW-effect to be derived within the framework of the same formalism as derived for gravitomagnetic lensing and reduces the iSW-effect to a second-order lensing phenomenon. The three-dimensional power spectra are projected by means of a generalized Limber-equation to yield the angular power spectra. Gravitomagnetic corrections to the weak-lensing spectrum are negligible at currently accessible scales, and cosmic-variance considerations suggest that the detection of the iSW-effect's contribution to the cosmic microwave background angular power spectrum is too small to be detectable at multipoles probed by the Planck satellite.     

Weak gravitational lensing in the standard cold dark matter model, using an algorithm for three-dimensional shear

We investigate the effects of weak gravitational lensing in the standard cold dark matter cosmology, using an algorithm that evaluates the shear in three dimensions. The algorithm has the advantage of variable softening for the particles, and our method allows the appropriate angular diameter distances to be applied to every evaluation location within each three-dimensional simulation box. We investigate the importance of shear in the distance–redshift relation, and find it to be very small. We also establish clearly defined values for the smoothness parameter in the relation, finding its value to be at least 0.83 at all redshifts in our simulations. From our results, obtained by linking the simulation boxes back to source redshifts of 4, we are able to observe the formation of structure in terms of the computed shear, and also note that the major contributions to the shear come from a very broad range of redshifts. We show the probability distributions for the magnification, source ellipticity and convergence, and also describe the relationships amongst these quantities for a range of source redshifts. We find a broad range of magnifications and ellipticities; for sources at a redshift of 4, 97.5 per cent of all lines of sight show magnifications up to 1.39 and ellipticities up to 0.23. There is clear evidence that the magnification is not linear in the convergence, as might be expected for weak lensing, but contains contributions from higher order terms in both the convergence and the shear. Our results for the one-point distribution functions are generally different from those obtained by other authors using two-dimensional (planar) approaches, and we suggest reasons for the differences. Our magnification distributions for sources at redshifts of 1 and 0.5 are also very different from the results used by other authors to assess the effect on the perceived value of the deceleration parameter, and we briefly address this question.     

Evolution of the dark matter distribution with three-dimensional weak lensing

We present a direct detection of the growth of large-scale structure, using weak gravitational lensing and photometric redshift data from the COMBO-17 survey. We use deep R -band imaging of two  0.5 × 0.5 deg²  fields, affording shear estimates for over 52 000 galaxies; we combine these with photometric redshift estimates from our 17-band survey, in order to obtain a 3D shear field. We find theoretical models for evolving matter power spectra and correlation functions, and fit the corresponding shear correlation functions to the data as a function of redshift. We detect the evolution of the power at the 4.7σ level given reasonable priors, and measure the rate of evolution for  0 < z < 1  . We also fit correlation functions to our 3D data as a function of cosmological parameters σ₈ and  Ω_Λ  . We find joint constraints on  Ω_Λ  and σ₈, demonstrating an improvement in accuracy by ≃40 per cent over that available from 2D weak lensing for the same area.     

Revisiting the magnification of type Ia supernovae with SDSS

We cross-correlate the sample of type Ia supernovae from Riess A. G. et al. with the SDSS DR2 photometric galaxy catalogue. In contrast to recent work, we find no detectable correlation between supernova magnitude and galaxy overdensity on scales ranging between 1 and 10 arcmin. Our results are in accord with theoretical expectations for gravitational lensing of supernovae by large-scale structure. Future supernova surveys such as SNAP will be capable of detecting unambiguously the predicted lensing signal.     

Probing the dark side of the Universe with weak gravitational lensing effects

Arising from gravitational deflections of light rays by large-scale structures in the Universe, weak-lensing effects have been recognized as one of the most important probes in cosmological studies. In this paper, we review the main progress in weak-lensing analyses, and discuss the challenges in future investigations aiming to understand the dark side of the Universe with unprecedented precisions.     

Probing the gravity-induced bias with weak lensing: test of analytical results against simulations

Future weak lensing surveys will directly probe the density fluctuation in the Universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field, we show that the bias associated with the convergence field can be directly related to the bias associated with the statistics of underlying overdense objects. This will provide us with a direct method to study the gravity-induced bias in galaxy clustering. Based on our analytical results, which use the hierarchical Ansatz for non-linear clustering, we study how such a bias depends on the smoothing angle and the source redshift. We compare our analytical results with ray-tracing experiments through N -body simulations of four different realistic cosmological scenarios, and find a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity-induced bias in galaxy clustering.