Astrophysical Implications of the Superstring-Inspired E_6 Unification and Shadow Theta-Particles

We have developed a concept of parallel existence of the ordinary (O) and mirror (M), or shadow (Sh) worlds. E_6 unification, inspired by superstring theory, restores the broken mirror parity at the scale ~ 10^18 GeV. With the aim to explain the tiny cosmological constant, we consider the breakings: E_6 -> SO(10) X U(1)_Z - in the O-world, and E'_6 -> SU(6)' X SU(2)'_\theta - in the Sh-world. We assume the existence of shadow \theta-particles and the low energy symmetry group SU(3)'_C X SU(2)'_L X SU(2)'_\theta X U(1)'_Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)'_\theta group with massless gauge fields, "thetons", has a macroscopic confinement radius 1/\Lambda'_\theta. The assumption that \Lambda'_\theta\approx 2.3 X 10^-3 eV explains the tiny cosmological constant given by recent astrophysical measurements. Searching for the Dark Matter (DM), it is possible to observe and study various signals of theta-particles.Comment: 6 pages, 2 figures, presented at "Invisble Universe International Conference", Palais de l'UNESCO, Paris, France, June 29 - July 3, 200

Standard Model and Graviweak Unification with (Super)Renormalizable Gravity. Part I: Visible and Invisible Sectors of the Universe

We develop a self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and invisible sectors of our Universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.Comment: 27 page

Mirror World and Superstring-Inspired Hidden Sector of the Universe, Dark Matter and Dark Energy

We develop a concept of parallel existence of the ordinary (O) and hidden (H) worlds. We compare two cases: 1) when the hidden sector of the Universe is a mirror counterpart of the ordinary world, and 2) when it is a superstring-inspired shadow world described, in contrast to the mirror world, by a symmetry group (or by a chain of groups), which does not coincide with the ordinary world symmetry group. We construct a cosmological model assuming the existence of the superstring-inspired E_6 unification, broken at the early stage of the Universe to SO(10)\times U(1)_Z - in the O-world, and to SU(6)'\times SU(2)'_\theta - in the H-world. As a result, we obtain the low energy symmetry group G'_SM\times SU(2)'_\theta in the shadow world, instead of the Standard Model group G_SM existing in the O-world. The additional non-Abelian SU(2)'_\theta group with massless gauge fields, "thetons", is responsible for dark energy. Considering a quintessence model of cosmology with an inflaton \sigma and an axion a_\theta, which is a pseudo Nambu-Goldstone boson induced by the SU(2)'_\theta-group anomaly, we explain the origin of Dark Energy, Dark Matter and Ordinary Matter. In the present model we review all cosmological epochs (inflation, reheating, recombination and nucleosynthesis), and give our version of the baryogenesis. The cosmological constant problem is also briefly discussed.Comment: 29 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1105.6286 and arXiv:1010.274

Solution of the Stochastic Langevin Equations for Clustering of Particles in Turbulent Flows in Terms of Wiener Path Integral

We propose to take advantage of using the Wiener path integrals as the formal solution for the joint probability densities of coupled Langevin equations describing particles suspended in a fluid under the effect of viscous and random forces. Our obtained formal solution, giving the expression for the Lyapunov exponent, i) will provide the description of all the features and the behaviour of such a system, e.g. the aggregation phenomenon recently studied in the literature using appropriate approximations, ii) can be used to determine the occurrence and the nature of the aggregation - non-aggregation phase transition which we have shown for the one-dimensional case and iii) allows the use of a variety of approximative methods appropriate for the physical conditions of the problem such as instanton solutions in the WKB approximation in the aggregation phase for the one-dimensional case as presented in this paper. The use of instanton approximation gives the same result for the Lyapunov exponent in the aggregation phase, previously obtained by other authors using a different approximative method. The case of non-aggregation is also considered in a certain approximation using the general path integral expression for the one-dimensional case.Comment: 18 pages; added section III C containing WKB method (instanton approximation) for the evaluation of the path integral in the aggregation, as well as non-aggregation, phase

Riemannian Geometry of Noncommutative Surfaces

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced and it is shown that the connections are metric-compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analogue of the first and second Bianchi identities. As examples, noncommutative analogues of the sphere, torus and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version to appear in J. Math. Phy

Thermal Casimir-Polder interaction of different atoms with graphene

The thermal correction to the energy of Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much smaller than the gap parameter (alternatively, larger or of the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He, Na, Rb, and Cs with graphene described by both the hydrodynamic and Dirac models. It is shown that in exact computations using the Dirac model, one should use the polarization operator at nonzero temperature. The computational results for the Casimir-Polder free energy obtained in the framework of hydrodynamic model of graphene are several times larger than in the Dirac model within the separation region below 2$\mu$m. We conclude that the theoretical predictions following from the two models can be reliably discriminated in experiments on quantum reflection of different atoms on graphene.Comment: 19 pages, 6 figures, to appear in Phys. Rev.

An Arena for Model Building in the Cohen-Glashow Very Special Relativity

The Cohen-Glashow Very Special Relativity (VSR) algebra [arXiv:hep-ph/0601236] is defined as the part of the Lorentz algebra which upon addition of CP or T invariance enhances to the full Lorentz group, plus the space-time translations. We show that noncommutative space-time, in particular noncommutative Moyal plane, with light-like noncommutativity provides a robust mathematical setting for quantum field theories which are VSR invariant and hence set the stage for building VSR invariant particle physics models. In our setting the VSR invariant theories are specified with a single deformation parameter, the noncommutativity scale \Lambda_{NC}. Preliminary analysis with the available data leads to \Lambda_{NC}\gtrsim 1-10 TeV. This note is prepared for the Proceedings of the G27 Mathematical Physics Conference, Yerevan 2008, and is based on arXiv:0806.3699[hep-th].Comment: Presented by M.M.Sh-J. in the G27 Mathematical Physics Conference, Yerevan 2008 as the 4th Weyl Prize Ceremony Tal

Superstring-Inspired E_6 Unification, Shadow Theta-Particles and Cosmology

We construct a new cosmological model considering the superstring-inspired E_6 unification in the 4-dimensional space at the early stage of the Universe. We develop a concept of parallel existence in Nature of the ordinary and shadow worlds with different cosmological evolutions.Comment: 7 page