We discuss the hypothesis that a large (or even a major) fraction of dark matter in the Universe consists of primordial black holes (PBH's). PBH's may arise from adiabatic quantum fluctuations appearing during inflation. We demonstrate that the inflation potential V ( 9 ) leading to the formation of a great number of PBH's should have a feature of the "plateaun-type in some range cpl < cp < cpz of the inflation field cp. The mass spectrum of PBH's for such a potential is calculated.PACS number(s): 98.80. Cq' 95.35.+d, 97.60.Lf, 98.70.V~

The interaction between a massive binary and a non-self-gravitating circumbinary accretion disc is considered. The shape of the stationary twisted disc produced by the binary is calculated. It is shown that the inner part of the disc must lie in the binary orbital plane for any value of the ivi@tfa.fy.chalmers.se viscosity.When the inner disc midplane is aligned with the binary orbital plane on the scales of interest and it rotates in the same sense as the binary, the modification to the disc structure and the rate of decay of the binary orbit, assumed circular, due to tidal exchange of angular momentum with the disc, are calculated. It is shown that the modified disc structure is well described by a self-similar solution of the non-linear diffusion equation governing the evolution of the disc surface density. The calculated time scale for decay of the binary orbit is always smaller than "accretion" time scale t acc = m/Ṁ (m is the mass of secondary component, andṀ is the disc accretion rate), and is determined by ratio of secondary mass m, assumed to be much smaller than the primary mass, the disc mass inside the initial binary orbit, and the form of viscosity in the disc.

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power‐law cusp. We show that the bulk of stars with a small angular‐momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so‐called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement. Our results show that for a primary black hole mass of ∼106–107 M⊙, the black hole mass‐ratio q > 10−2, cusp size ∼1 pc, the tidal disruption rate can be as large as ∼10−2–1 M⊙ yr−1. This is at least 102–104 times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical‐friction time‐scale, and it is rather short: ∼105 yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.

We consider the simple inflationary model with peculiarity in the form of "plateau" in the inflaton potential. We use the formalism of coarse-grained field in order to describe the production of metric perturbations h of an arbitrary amplitude, and obtain non-Gaussian probability function for such metric perturbations. We associate the spatial regions having large perturbations h ∼ 1 with the regions going to primordial black holes after inflation. We show that in our model the non-linear effects can lead to overproduction of the primordial black holes. PACS number(s): 98.80. Cq, 97.60.Lf, 98.70. Vc, 98.80.Hw