Below we will consider a new mechanism describing the early formation of PBHs, which serve as the nucleation centers in the subsequent formation of galaxies. This mechanism may prove to be free from dis-

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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.

We describe a mechanism of the primordial black holes formation that can explain the existence of a population of supermassive black holes in galactic bulges. The mechanism is based on the formation of black holes from closed domain walls. The origin of such domain walls could be a result of the evolution of an effectively massless scalar field during inflation. The initial non-equilibrium distribution of the scalar field imposed by background de-Sitter fluctuations gives rise to the spectrum of black holes, which covers a wide range of masses -from superheavy ones down to deeply subsolar. The primordial black holes of smaller masses are concentrated around the most massive ones within a fractal-like cluster.

We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a 3 slow-change approximation) can work with rather a general form of the gravitational action. As examples, we consider pure gravity with Lagrangians quadratic and cubic in the scalar curvature and some more complex ones in a simple Kaluza-Klein framework. After a transition to the 4D Einstein conformal frame, this results in effective scalar field theories with certain effective potentials, which in many cases possess positive minima providing stable small-size extra dimensions. Estimates made in the original (Jordan) conformal frame show that the problem of a small value of the cosmological constant in the present Universe is softened in this framework but is not solved completely.Short title: Self-stabilization of extra dimensions PACS numbers: 04.50.+h; 98.80.Cq

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.

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We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the V ∼ x 4 potential. The renormalized action is relevant for quantum chaos and quantum instantons.