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 $R^2$ 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 ${|x>}$, for an alternative countable basis ${|n>}$. 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 ${\cal C}$ gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl-Heisenberg algebra $h(1)$ with ${\cal C}=0$ for Hermite polynomials and $su(1,1)$ with ${\cal C}=-1/4$ for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the ${\cal L}^2$ functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space ${\cal L}^2$ and, in particular, generalized coherent polynomials are thus obtained.Comment: 11 page