The ΛCDM model, or concordance cosmology, as it is often called, is a paradigm at its maturity. It is clearly able to describe the universe at large scale, even if some issues remain open, such as the cosmological constant problem, the small-scale problems in galaxy formation, or the unexplained anomalies in the CMB. ΛCDM clearly shows difficulty at small scales, which could be related to our scant understanding, from the nature of dark matter to that of gravity; or to the role of baryon physics, which is not well understood and implemented in simulation codes or in semi-analytic models. At this stage, it is of fundamental importance to understand whether the problems encountered by the ΛDCM model are a sign of its limits or a sign of our failures in getting the finer details right. In the present paper, we will review the small-scale problems of the ΛCDM model, and we will discuss the proposed solutions and to what extent they are able to give us a theory accurately describing the phenomena in the complete range of scale of the observed universe.

A promising energy range to look for angular correlations between cosmic rays of extragalactic origin and their sources is at the highest energies, above a few tens of EeV (1 EeV ≡ 10¹⁸ eV). Despite the flux of these particles being extremely low, the area of ∼3000 km² covered at the Pierre Auger Observatory, and the 17 yr data-taking period of the Phase 1 of its operations, have enabled us to measure the arrival directions of more than 2600 ultra-high-energy cosmic rays above 32 EeV. We publish this data set, the largest available at such energies from an integrated exposure of 122,000 km² sr yr, and search it for anisotropies over the 3.4π steradians covered with the Observatory. Evidence for a deviation in excess of isotropy at intermediate angular scales, with ∼15° Gaussian spread or ∼25° top-hat radius, is obtained at the 4σ significance level for cosmic-ray energies above ∼40 EeV.

We study the structure of compact objects that contain non-self annihilating, self-interacting dark matter admixed with ordinary matter made of neutron star and white dwarf materials. We extend the previous work [ Phys. Rev. D 92, 123002 (2015)] on these dark compact objects by analyzing the effect of weak and strongly interacting dark matter with particle masses in the range of 1–500 GeV, so as to set some constraints in the strength of the interaction and the mass of the dark matter particle. We find that the total mass of the compact objects increases with decreasing dark matter particle mass. In the strong interacting case and for dark matter particle masses in the range 1–10 GeV, the total mass of the compact objects largely exceeds the $2M_{\odot }$ constraint for neutron star masses and the nominal $1M_{\odot }$ for white dwarfs, while for larger dark matter particle masses or in the weakly interacting case the compact objects show masses in agreement or smaller than these constraints, thus hinting at the exclusion of strongly self-interacting dark matter of masses 1–10 GeV in the interior of these compact objects. Moreover, we observe that the smaller the dark matter particle mass, the larger the quantity of dark matter captured is, putting constraints on the dark matter mass trapped in the compact objects so as to fulfill $\simeq 2M_{\odot }$ observations. Finally, the inhomogeneity of distribution of dark matter in the Galaxy implies a mass dependence of compact objects from the environment which can be used to put constraints on the characteristics of the Galaxy halo DM profile and on particle mass. In view of these results, we discuss the formation of the dark compact objects in an homogeneous and nonhomogeneous dark matter environment.

We study the effect of shear and rotation on results previously obtained dealing with the application of the spherical collapse model (SCM) to generalized Chaplygin gas (gCg)-dominated universes. The system is composed of baryons and gCg and the collapse is studied for different values of the parameter $\alpha$ of the gCg. We show that the joint effect of shear and rotation is that of slowing down the collapse with respect to the simple SCM. This result is of utmost importance for the so-called unified dark matter models, since the described slowdown in the growth of density perturbations can solve one of the main problems of the quoted models, namely the instability described in previous papers [e.g., H. B. Sandvik et al., Phys. Rev. D 69, 123524 (2004)] at the linear perturbation level.

This review aims at proposing to the field an overview of the Cusp-core problem, including a discussion of its advocated solutions, assessing how each can satisfactorily provide a description of central densities. Whether the Cusp-core problem reflects our insufficient grasp on the nature of dark matter, of gravity, on the impact of baryonic interactions with dark matter at those scales, as included in semi-analytical models or fully numerical codes, the solutions to it can point either to the need for a paradigm change in cosmology, or to to our lack of success in ironing out the finer details of the ΛCDM paradigm.

In this paper, we analysed the correlation between the central surface density and the halo core radius of galaxies, and cluster of galaxies dark matter (DM) haloes, in the framework of the secondary infall model. We used Del Popolo secondary infall model taking into account ordered and random angular momentum, dynamical friction and DM adiabatic contraction to calculate the density profile of haloes, and then these profiles are used to determine the surface density of DM haloes. The main result is that r_* (the halo characteristic radius) is not a universal quantity as claimed by Donato et al. and Gentile et al. On the contrary, we find a correlation with the halo mass M₂₀₀ in agreement with Cardone & Tortora, Boyarsky et al. and Napolitano, Romanowsky & Tortora, but with a significantly smaller scatter, namely 0.16 ± 0.05. We also consider the baryon column density finding this latter being indeed a constant for low-mass systems, such as dwarfs, but correlating with mass with a slope of α = 0.18 ± 0.05. In the case of the surface density of DM for a system composed only of DM, as in dissipationless simulations, we get α = 0.20 ± 0.05. These results leave little room for the recently claimed universality of (dark and stellar) column density.