The Primordial Black Holes (PBHs) are a well-established probe for new physics in the very early Universe. We discuss here the possibility of PBH agglomeration into clusters that may have several prominent observable features. The clusters can form due to closed domain walls appearance in the natural and hybrid inflation models whose subsequent evolution leads to PBH formation. The dynamical evolution of such clusters discussed here is of crucial importance. Such a model inherits all the advantages of uniformly distributed PBHs, like possible explanation of supermassive black holes existence (origin of the early quasars), the binary black hole mergers registered by LIGO/Virgo through gravitational waves, which could provide ways to test the model in future, the contribution to reionization of the Universe. If PBHs form clusters, they could alleviate or completely avoid existing constraints on the abundance of uniformly distributed PBHs, thus allowing PBH to be a viable dark matter candidate. Most of the existing constraints on uniform PBH density should be re-considered to the case of PBH clustering. Furthermore, unidentified cosmic gamma-ray point-like sources could be (partially) accounted. We conclude that models leading to PBH clustering are favored compared to models predicting the uniform distribution of PBHs.

The nonbaryonic dark matter of the Universe is assumed to consist of new stable forms of matter. Their stability reflects symmetry of micro world and mechanisms of its symmetry breaking. In the early Universe heavy metastable particles can dominate, leaving primordial black holes (PBHs) after their decay, as well as the structure of particle symmetry breaking gives rise to cosmological phase transitions, from which massive black holes and/or their clusters can originate. PBHs can be formed in such transitions within a narrow interval of masses about 10 17 g and, avoiding severe observational constraints on PBHs, can be a candidate for the dominant form of dark matter. PBHs in this range of mass can give solution of the problem of reionization in the Universe at the redshift z ∼ 5 . . . 10. Clusters of massive PBHs can serve as a nonlinear seeds for galaxy formation, while PBHs evaporating in such clusters can provide an interesting interpretation for the observations of point-like gamma-ray sources. Analysis of possible PBH signatures represents a universal probe for super-high energy physics in the early Universe in studies of indirect effects of the dark matter.

Here we briefly review possible indirect effects of dark matter (DM) of the Universe. It includes effects in cosmic rays (CR): first of all, the positron excess at ∼ 500 GeV and possible electron-positron excess at 1-1.5 TeV. We tell that the main and least model-dependent constraint on such possible interpretation of CR effects goes from gamma-ray background. Even ordinary e + e − mode of DM decay or annihilation produces prompt photons (FSR) so much that it leads to contradiction with data on cosmic gamma-rays. We present our attempts to possibly avoid gamma-ray constraint. They concern peculiarities of both space distribution of DM and their physics. The latter involves complications of decay/annihilation modes of DM, modifications of Lagrangian of DM-ordinary matter interaction, and inclusion of mode with identical fermions in final state. In this way, no possibilities to suppress were found yet except, possibly, mode with identical fermions. While the case of spatial distribution variation allows achieving consistency between different data. Also we consider stable form of dark matter which can interact with baryons. We show which constraint such DM candidate can get from damping effect in plasma during large scale structure formation in comparison with other existing constraints.

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Cold dark matter (DM) scenario may be cured of several problems by involving self-interaction of dark matter. Viability of the models of long-range interacting DM crucially depends on the effectiveness of recombination of the DM particles, making thereby their interaction short-range. Usually in numeric calculations, recombination is described by cross section obtained on a feasible quantum level. However in a wide range of parameter values, a classical treatment, where the particles are bound due to dipole radiation, is applicable. The cross sections, obtained in both approaches, are very different and lead to diverse consequences. Classical cross section has a steeper dependence on relative velocity, what leads to the fact that, after decoupling of DM particles from thermal background of "dark photons" (carriers of DM long-range interaction), recombination process does not "freeze out", diminishing gradually density of unbound DM particles. Our simplified estimates show, that at the taken parameter values (the mass of DM particle is 100 GeV, interaction constant is 100 −1 , and quite natural assumptions on initial conditions, from which the result is very weakly dependent) the difference in residual density reaches about 5 orders of magnitude on pre-galactic stage. This estimate takes into account thermal effects induced by dipole radiation and recombination, which resulted in the increase of both temperature and density of DM particles by a half order of magnitude.The models of self-interacting dark matter (DM) have aroused a lot of interest in the last time [1][2][3][4][5][6][7][8][9][10][11]. DM with long-range interaction (referring hereafter as to y-interaction) seems to be able to escape several problems of ordinary cold dark matter (CDM) scenario, such as an overproduction of subhalos and cuspy density profile in them [6,8,12,13]. At the same time, an ellipticity of big halos is not spoiled at some model parameters [8]. An enhancement of annihilation signal in the Galaxy (so called Sommerfeld-Gamov-Sakharov enhancement [14-16]), considered for the first time (to our knowledge) in [17], is one more possible bonus of the models of question. Analysis of recent observations of forming galactic cluster Abell 3827 also favours self-interacting DM [18]. Origin of supermassive black holes can be connected with an existence of DM component with strong self-interaction [19]. Generally, models with dissipative form of DM as sub-component find more applications [20,21].Essential feature of cosmological evolution of y-interacting DM is a formation of atomic-like bound states by DM particles with opposite y-charges. If oppositely y-charged particles are particle (a) and anti-particle (b =ā), then they annihilate, what may drastically affect their residual density [5,12,22]. If the bound particles are different species (a and b =ā) so bound state is stable, then depending on relative amount of bound and unbound particles, as it is obtained by the period of large scale structure formation, DM dynamics