Exact solution of the relativistic magnetohydrodynamic equations in the background of a plane gravitational wave with combined polarization

We obtain an exact solution of the self-consistent relativistic magnetohydrodynamic equations for an anisotropic magnetoactive plasma in the background of a plane gravitational wave metric (PGW) with an arbitrary polarization. It is shown that, in the linear approximation in the gravitational wave amplitude, only the $\mathbf{e_+}$ polarization of the PGW interacts with a magnetoactive plasma.Comment: 5 pages, 8 reference

Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

Let $\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\Phi$, $U$ be its maximal unipotent subgroup and $\mathfrak{u}$ be the Lie algebra of $U$. Let $D$ be an orthogonal subset of $\Phi$ and $\Omega$ be a coadjoint orbit of $U$ associated with $D$. We construct a polarization of $\mathfrak{u}$ at the canonical form on $\Omega$. We also find the dimension of $\Omega$ in terms of the Weyl group of $\Phi$. As a corollary, we determine all possible dimensions of irreducible complex represenations of the group $U$ for the case of finite field $k$.Comment: 11 page

Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Cosmological evolution of statistical system of scalar charged particles

© 2015, Springer Science+Business Media Dordrecht. In the paper we consider the macroscopic model of plasma of scalar charged particles, obtained by means of the statistical averaging of the microscopic equations of particle dynamics in a scalar field. On the basis of kinetic equations, obtained from averaging, and their strict integral consequences, a self-consistent set of equations is formulated which describes the self-gravitating plasma of scalar charged particles. It was obtained the corresponding closed cosmological model which also was numerically simulated for the case of one-component degenerated Fermi gas and two-component Boltzmann system. It was shown that results depend weakly on the choice of a statistical model. Two specific features of cosmological evolution of a statistical system of scalar charged particles were obtained with respect to cosmological evolution of the minimal interaction models: appearance of giant bursts of invariant cosmological acceleration Ω at the time interval 8⋅103–2⋅104 tPl and strong heating (3–8 orders of magnitude) of a statistical system at the same times. The presence of such features can modify the quantum theory of generation of cosmological gravitational perturbations

Resonant interaction between gravitational waves, electromagnetic waves and plasma flows

In magnetized plasmas gravitational and electromagnetic waves may interact coherently and exchange energy between themselves and with plasma flows. We derive the wave interaction equations for these processes in the case of waves propagating perpendicular or parallel to the plasma background magnetic field. In the latter case, the electromagnetic waves are taken to be circularly polarized waves of arbitrary amplitude. We allow for a background drift flow of the plasma components which increases the number of possible evolution scenarios. The interaction equations are solved analytically and the characteristic time scales for conversion between gravitational and electromagnetic waves are found. In particular, it is shown that in the presence of a drift flow there are explosive instabilities resulting in the generation of gravitational and electromagnetic waves. Conversely, we show that energetic waves can interact to accelerate particles and thereby \emph{produce} a drift flow. The relevance of these results for astrophysical and cosmological plasmas is discussed.Comment: 12 pages, 1 figure, typos corrected and numerical example adde

Cosmological models with interacting components and mass-varying neutrinos

A model for a homogeneous and isotropic spatially flat Universe, composed of baryons, radiation, neutrinos, dark matter and dark energy is analyzed. We infer that dark energy (considered to behave as a scalar field) interacts with dark matter (either by the Wetterich model, or by the Anderson and Carroll model) and with neutrinos by a model proposed by Brookfield et al.. The latter is understood to have a mass-varying behavior. We show that for a very-softly varying field, both interacting models for dark matter give the same results. The models reproduce the expected red-shift performances of the present behavior of the Universe.Comment: 8 pages, 5 figures, to be published in Gravitation and Cosmolog

Leptogenesis with Heavy Majorana Neutrinos Reexamined

The mass term for Majorana neutrinos explicitly violates lepton number. Several authors have used this fact to create a lepton asymmetry in the universe by considering CP violating effects in the one loop self-energy correction for the decaying heavy Majorana neutrino. We compare and comment on the different approaches used to calculate the lepton asymmetry including those using an effective Hamiltonian and resummed propagators. We also recalculate the asymmetry in the small mass difference limit.Comment: 16 pages, LaTex, 1 figure included. 2 footnotes and 1 reference adde