We study the spherical collapse model for several dark-energy scenarios using the fully non-linear differential equation for the evolution of the density contrast within homogeneous spherical overdensities derived from Newtonian hydrodynamics. While mathematically equivalent to the more common approach based on the differential equation for the radius of the perturbation, this approach has substantial conceptual as well as numerical advantages. Among the most important are that no singularities at early times appear, which avoids numerical problems in particular in applications to cosmologies with dynamical and early dark energy, and that the assumption of time-reversal symmetry can easily be dropped where it is not strictly satisfied. We use this approach to derive the two parameters characterizing the spherical-collapse model, i.e. the linear density threshold for collapse δ c and the virial overdensity V , for a broad variety of dark-energy models and to reconsider these parameters in cosmologies with early dark energy. We find that, independently of the model under investigation, δ c and V are always very close to the values obtained for the standard CDM model, arguing that the abundance of and the mean density within non-linear structures are quite insensitive to the differences between dark-energy cosmologies. Regarding early dark energy, we thus arrive at a different conclusion than some earlier papers, including one from our group, and we explain why.

The galaxy cluster MACS J0717.5+3745 (z = 0.55) is the largest known cosmic lens, with complex internal structures seen in deep X-ray, Sunyaev-Zel'dovich effect and dynamical observations. We perform a combined weak and strong lensing analysis with wide-field BV R c i z Subaru/Suprime-Cam observations and 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH). We find consistent weak distortion and magnification measurements of background galaxies, and combine these signals to construct an optimally estimated radial mass profile of the cluster and its surrounding large-scale structure out to 5 Mpc/h. We find consistency between strong-lensing and weak-lensing in the region where these independent data overlap, < 500 kpc/h. The two-dimensional weak-lensing map reveals a clear filamentary structure traced by distinct mass halos. We model the lensing shear field with 9 halos, including the main cluster, corresponding to mass peaks detected above 2.5σ κ . The total mass of the cluster as determined by the different methods is M vir ≈ (2.8 ± 0.4) × 10 15 M . Although this is the most massive cluster known at z > 0.5, in terms of extreme value statistics we conclude that the mass of MACS J0717.5+3745 by itself is not in serious tension with ΛCDM, representing only a ∼ 2σ departure above the maximum simulated halo mass at this redshift.

For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z s = 2.0, we find that mergers increase the number of Einstein radii above 10 (20 ) by ∼35% (∼55%). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio ≥7.5 of those clusters with Einstein radii above 10 (20 ) increases by ∼45% (∼85%). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.