Zero average values of cosmological perturbations as an indispensable condition for the theory and simulations

We point out a weak side of the commonly used determination of scalar cosmological perturbations lying in the fact that their average values can be nonzero for some matter distributions. It is shown that introduction of the finite-range gravitational potential instead of the infinite-range one resolves this problem. The concrete illustrative density profile is investigated in detail in this connection.Comment: 5 pages, 2 figure

Decaying Dark Atom constituents and cosmic positron excess

We present a scenario where dark matter is in the form of dark atoms that can accomodate the experimentally observed excess of positrons in PAMELA and AMS-02 while being compatible with the constraints imposed on the gamma-ray flux from Fermi/LAT. This scenario assumes that the dominant component of dark matter is in the form of a bound state between a helium nucleus and a $-2$ particle and a small component is in the form of a WIMP-like dark atom compatible with direct searches in underground detectors. One of the constituents of this WIMP-like state is a $+2$ metastable particle with a mass of 1 TeV or slightly below that by decaying to $e^+e^+$, $\mu^+ \mu^+$ and $\tau^+ \tau^+$ produces the observed positron excess. These decays can naturally take place via GUT interactions. If it exists, such a metastable particle can be found in the next run of LHC. The model predicts also the ratio of leptons over baryons in the Universe to be close to -3.Comment: 20 pages, 4 figures, submitted to Advances in High Energy Physic

Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons

We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped atomic trap. We show that in the low-energy scattering regime, the scattering process degenerates to a total reflection suggesting an experimental realization of a famous model in theoretical physics - a one-dimensional gas of impenetrable bosons (``Tonks'' gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.Comment: 5 pages, 2 figures; list of atoms - candidates for the Tonks gas realisation is restricted to the positive scatt. length; Cs is excluded from the list; some new references added; minor changes in the text; accepted in PRL June 22, 199