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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.

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We discuss axion dark matter detection via two mechanisms: spontaneous decays and resonant conversion in neutron star magnetospheres. For decays, we show that the brightness temperature signal, rather than flux, is a less ambiguous measure for selecting candidate objects. This is owing principally to the finite beam width of telescopes which prevents one from being sensitive to the total flux from the object. With this in mind, we argue that the large surface-mass-density of the galactic center or the Virgo cluster center offer the best chance of improving current constraints on the axion-photon coupling via spontaneous decays. For the neutron star case, we first carry out a detailed study of mixing in magnetized plasmas. We derive transport equations for the axion-photon system via a controlled gradient expansion, allowing us to address inhomogeneous mass-shell constraints for arbitrary momenta. We then derive a nonperturbative Landau-Zener formula for the conversion probability valid across the range of relativistic and nonrelativistic axions and show that the standard perturbative resonant conversion amplitude is a truncation of this result in the nonadiabatic limit. Our treatment reveals that infalling dark matter axions typically convert nonadiabatically in magnetospheres. We describe the limitations of one-dimensional mixing equations and explain how three-dimensional effects activate new photon polarizations, including longitudinal modes and illustrate these arguments with numerical simulations in higher dimensions. We find that the bandwidth of the radio signal from neutron stars could be dominated by Doppler broadening from the oblique rotation of the neutron star if the axion is nonrelativistic in the conversion region. Therefore, we conclude that the radio signal from the resonant decay is weaker than previously thought, which means one relies on local density peaks to probe weaker axion-photon couplings.

Context. Strong lensing is one of the most direct probes of mass distribution in the inner regions of galaxy clusters. It can be used to constrain the density profiles and to measure the mass of the lenses. Moreover, the abundance of strong lensing events can be used to constrain structure formation and cosmological parameters through the so-called "arc-statistics" approach. However, several issues related to the use of strong lensing clusters in cosmological applications are still controversial, leading to the suspicion that several biases may affect this very peculiar class of objects. Aims. With this study we aim a better understanding of the properties of galaxy clusters that can potentially act as strong lenses. Methods. We do so by investigating the properties of a large sample of galaxy clusters extracted from the N-body/hydrodynamical simulation MareNostrum Universe. We perform ray-tracing simulations with each of them and identify those objects capable of producing strong lensing effects. We explore the correlation between the cross section for lensing and many properties of clusters, such as mass, three-dimensional and projected shapes, their concentrations, the X-ray luminosity, and the dynamical activity. Results. We quantify the minimal cluster mass required for producing both multiple images and large distortions. While we do not measure a significant excess of triaxiality in strong lensing clusters, we find that the probability of strong alignments between the major axes of the lenses and the line of sight is a growing function of the lensing cross section. In projection, the strong lenses appear rounder within R 200 , but we find that their cores tend to be more elliptical as the lensing cross section increases. As a result of the orientation bias, we also find that the cluster concentrations estimated from the projected density profiles tend to be biased high. The X-ray luminosity of strong lensing clusters tend to be higher than for normal lenses of similar mass and redshift. This is particularly significant for the least massive lenses. Finally, we find that the strongest lenses generally exhibit an excess of kinetic energy within the virial radius, thus indicating that they are more dynamically active than the usual clusters. Conclusions. We conclude that strong lensing clusters are a very peculiar class of objects, affected by many selection biases that need to be properly modeled when using them to study the inner structure of galaxy clusters or to constrain the cosmological parameters.