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.

We show that an inhomogeneous compact extra space possesses two necessary features their existence does not contradict the observable value of the cosmological constant Λ 4 in pure f (R) theory, and the extra dimensions are stable relative to the "radion mode" of perturbations, the only mode considered. For a two-dimensional extra space, both analytical and numerical solutions for the metric are found, able to provide a zero or arbitrarily small Λ 4 . A no-go theorem has also been proved, that maximally symmetric compact extra spaces are inconsistent with 4D Minkowski space in the framework of pure f (R)With their whole diversity, the models involving extra dimensions must overcome two common problems: the smallness of the cosmological constant they induce [1,2], and the stability of an extra space metric. Observations indicate that our Universe is nowadays expanding with acceleration [3], which can be explained in Einstein gravity by the existence of a cosmological constant Λ ∼ 10 −3 eV 4 or something very close to it, called dark energy, see a review in [4]. We live in space-time approximately described by the de Sitter metric, which is, in a sense, extremely close to the Minkowski one. Any study should be in agreement with this observational fact.There are a lot of approaches to solving the problem: one introduces scalar fields (see, e.g., [5]), form fields [6], invariants other than powers of R [7], or considers compact extra spaces with zero curvature, e.g., Calabi-Yau manifolds [8], one-dimensional extra spaces [9] and flat tori [10]. As shown in [11], insertion of form fields leads to an extra space with the metric of a sphere with a deficit angle and an observationally acceptable value of Λ. The study appeared recently is based on Horndeski scalar-tensor theories of gravity involving Poincare invariance breaking [12] that comes together with a self-tuning mechanism driven by scalar field dynamics. It was pointed out by Babichev and Esposito-Farese that a local deviation from general relativity would rule out a model even with good Λ tuning. The accordance of Hordeski-like theories (generalized Gallileon) with solar system gravity tests were studied in [13].On the other hand, inhomogeneous extra spaces are a promising tool that could underlie such effects of low-energy physics as the formation of fermion generations [16], explanation of dark matter [14], and creation of branes [15]. Evidently, this direction deserves a deep study. In particular, both problems mentioned above, stability of compact extra dimensions and smallness of the cosmological constant, should be solved at least at the classical level. In this paper we discuss these problems for an inhomogeneous (deformed) compact extra space with a nonzero Ricci scalar, related to [14,15].This study is performed on the basis of pure multidimensional f (R) gravity. No other tools listed above are used. The interest in f (R) theories is motivated by inflationary scenarios starting from Starobinsky's pioneering work [19]. A number of viable f (R) models i...

We elaborate the possibility for a deformed extra space to be considered as the dark matter candidate. To perform calculations a class of two-dimensional extra metrics was considered in the framework of the multidimensional gravity. It was shown that there exists a family of stationary metrics of the extra space possessing point-like defect. Estimation of cross section of scattering of a particle of the ordinary matter on a spatial domain with deformed extra space is in agreement with the observational constraints.Comment: 12 pages, 5 figures; V2: some changes to match version published in IJMP

We study a class of two-dimensional compact extra spaces isomorphic to the sphere S 2 in the framework of multidimensional gravitation. We show that there exists a family of stationary metrics that depend on the initial (boundary) conditions. All these geometries have a singular point. We also discuss the possibility for these deformed extra spaces to be considered as dark matter candidates.

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