Axionic extension of the Einstein-aether theory

We extend the Einstein-aether theory to take into account the interaction between a pseudoscalar field, which describes the axionic dark matter, and a time-like dynamic unit vector field, which characterizes the velocity of the aether motion. The Lagrangian of the Einstein-aether-axion theory includes cross-terms based on the axion field and its gradient four-vector, on the covariant derivative of the aether velocity four-vector, and on the Riemann tensor and its convolutions. We follow the principles of the Effective Field theory, and include into the Lagrangian of interactions all possible terms up to the second order in the covariant derivative. Interpretation of new couplings is given in terms of irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. A spatially isotropic and homogeneous cosmological model with dynamic unit vector field and axionic dark matter is considered as an application of the established theory; new exact solutions are discussed, which describe models with a Big Rip, Pseudo Rip and de Sitter-type asymptotic behavior.Comment: 15 pages, 0 figures, accepted for publication in Physical Review

Curvature Coupling and Accelerated Expansion of the Universe

A new exactly solvable model for the evolution of relativistic kinetic system interacting with an internal stochastic reservoir under the influence of a gravitational background expansion is established. This model of self-interaction is based on the relativistic kinetic equation for the distribution function defined in the extended phase space. The supplementary degree of freedom is described by the scalar stochastic variable (Langevin source), which is considered to be the constructive element of the effective one-particle force. The expansion of the Universe is shown to be accelerated for the suitable choice of the non-minimal self-interaction force.Comment: 12 pages, no figure

Ideal webs, moduli spaces of local systems, and 3d Calabi-Yau categories

A decorated surface S is an oriented surface with punctures and a finite set of marked points on the boundary, such that each boundary component has a marked point. We introduce ideal bipartite graphs on S. Each of them is related to a group G of type A, and gives rise to cluster coordinate systems on certain spaces of G-local systems on S. These coordinate systems generalize the ones assigned to ideal triangulations of S. A bipartite graph on S gives rise to a quiver with a canonical potential. The latter determines a triangulated 3d CY category with a cluster collection of spherical objects. Given an ideal bipartite graph on S, we define an extension of the mapping class group of S which acts by symmetries of the category. There is a family of open CY 3-folds over the universal Hitchin base, whose intermediate Jacobians describe the Hitchin system. We conjecture that the 3d CY category with cluster collection is equivalent to a full subcategory of the Fukaya category of a generic threefold of the family, equipped with a cluster collection of special Lagrangian spheres. For SL(2) a substantial part of the story is already known thanks to Bridgeland, Keller, Labardini-Fragoso, Nagao, Smith, and others. We hope that ideal bipartite graphs provide special examples of the Gaiotto-Moore-Neitzke spectral networks.Comment: 60 page

The Catholic Core of a Celebrated Composition

Despite an undeviating opinion on the subject, his greatest work The Lord of the Rings, is replete with free-floating allegory to Christian characters. Characters and situations that suggest Biblical situations, both narratively and on the level of spirituality and ethics. Each character within biblical text correlates with one or more characters in Tolkien’s work, thus free floating. Tolkien is a devoutly religious author who processes the world, including his own fantasies, through the lens of his faith. While Tolkien draws from different elements of theology in several different ways—such as interchanging his characters to represent various aspects of key Biblical figures—it is clear that Tolkien assigned a moral, free-flowing, yet religious allegorical backbone to his work

The Melianthaceous seed and its Rhamnaceous affinity

. La semilla de Melianthaceae y su afinidad con Rhamnaceae. En el presente trabajo, se ha estudiado la anatomia y morfología de la semilla de Bersama (Bersamataceae) y Melianthus (Melianthaceae) con el objeto de clarificar su posición sistemática. La exotesta de Bersama y Melianthus, con una empalizada de células de Malpighi bien diferenciada, abundante endosperma y embrión recto y escasamente diferenciado, muestra ciertas afinidades con la exotesta albuminosa de las semillas de Rhamnaceae y Elaeagnaceae. Utilizando también datos carpológicos, florales y morfológico-vegetativos adicionales, se sugiere que Bersamataceae, junto con Melianthaceae y Rhamnaceae/Elaeagnaceae constituyen una ramificación lateral relíctica de un ancestro roside exo-mesotestado. La morfología y anatomía de las semillas evidencian la anómala y tradicional inclusión de Bersama y Melianthus en el orden Sapindales, cuyas semillas presentan diferente pautas en la estructura de la espermodermis y en la vascularización de la misma. La anatomía de la semilla, no confirma ninguna de las relaciones que se han sugerido, alternativamente, con Lardizabalaceae exo-mesotestales ni con Malvales exotegmicos. Por otra parte, consideramos insostenibles las afinidades con Celastrales exotégmicos, que han sido consideradas como una posible conexión entre Rosales arcaicos exo-mesotestados y Rhamnales/Elaeagnales exotestados. Se sugiere que ambas familias, Bersamataceae y Melianthaceae, constituyen el orden Melianthales que, junto con Rhamnaceae (Rhamnales, s. e.) y Elaeagnaceae (Elaeagnales) representan remanentes avanzados de un phyllum profusamente ramificado, cuyas relaciones se remontan directamente hacia Fabales, pasando por Rosales, Sapindales, Icacinales y Celastrales

Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G.Comment: 12 pages, LaTe