2,710 research outputs found
Non-singular Universes a la Palatini
It has recently been shown that f(R) theories formulated in the Palatini
variational formalism are able to avoid the big bang singularity yielding
instead a bouncing solution. The mechanism responsible for this behavior is
similar to that observed in the effective dynamics of loop quantum cosmology
and an f(R) theory exactly reproducing that dynamics has been found. I will
show here that considering more general actions, with quadratic contributions
of the Ricci tensor, results in a much richer phenomenology that yields
bouncing solutions even in anisotropic (Bianchi I) scenarios. Some implications
of these results are discussed.Comment: 4 pages, no figures. Contribution to the Spanish Relativity Meeting
(ERE2010), 6-10 Sept. Granada, Spai
Nonsingular electrovacuum solutions with dynamically generated cosmological constant
We consider static spherically symmetric configurations in a Palatini
extension of General Relativity including and Ricci-squared terms, which
is known to replace the central singularity by a wormhole in the electrovacuum
case. We modify the matter sector of the theory by adding to the usual Maxwell
term a nonlinear electromagnetic extension which is known to implement a
confinement mechanism in flat space. One feature of the resulting theory is
that the non-linear electric field leads to a dynamically generated
cosmological constant. We show that with this matter source the solutions of
the model are asymptotically de Sitter and possess a wormhole topology. We
discuss in some detail the conditions that guarantee the absence of
singularities and of traversable wormholes.Comment: 7 double-column pages; v2: several changes in abstract and
introductio
Biodiversity, taxonomy and metagenomics
GenBank (Benson et al. 2013) is a database that
contains genetic sequences of species. Godfray
(2007) proposed that metagenomics can replace taxonomy
in identifying specimens. Indeed, giving
names to specimens is not the primary role of taxonomy,
the discipline being devoted to the description
of new species and to reconstruction of
phylogenies, focusing on both genotypes and phenotypes.
So, the use of metagenomics for routinary
species identification is a welcome technological aid
to the study of biodiversity, freeing taxonomists from
the burden of sorting and identifying biological
material
Coherent Orthogonal Polynomials
We discuss as a fundamental characteristic of orthogonal polynomials like the
existence of a Lie algebra behind them, can be added to their other relevant
aspects. At the basis of the complete framework for orthogonal polynomials we
put thus --in addition to differential equations, recurrence relations, Hilbert
spaces and square integrable functions-- Lie algebra theory.
We start here from the square integrable functions on the open connected
subset of the real line whose bases are related to orthogonal polynomials. All
these one-dimensional continuous spaces allow, besides the standard uncountable
basis , for an alternative countable basis . The matrix elements
that relate these two bases are essentially the orthogonal polynomials: Hermite
polynomials for the line and Laguerre and Legendre polynomials for the
half-line and the line interval, respectively.
Differential recurrence relations of orthogonal polynomials allow us to
realize that they determine a unitary representation of a non-compact Lie
algebra, whose second order Casimir gives rise to the second order
differential equation that defines the corresponding family of orthogonal
polynomials. Thus, the Weyl-Heisenberg algebra with for
Hermite polynomials and with for Laguerre and
Legendre polynomials are obtained.
Starting from the orthogonal polynomials the Lie algebra is extended both to
the whole space of the functions and to the corresponding
Universal Enveloping Algebra and transformation group. Generalized coherent
states from each vector in the space and, in particular,
generalized coherent polynomials are thus obtained.Comment: 11 page
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