Dark Energy in vector-tensor theories of gravity

We consider a general class of vector-tensor theories of gravity and show that solutions with accelerated expansion and a future type III singularity are a common feature in these models. We also show that there are only six vector-tensor theories with the same small scales behavior as General Relativity and, in addition, only two of them can be made completely free from instabilities. Finally, two particular models as candidates for dark energy are proposed: on one hand, a cosmic vector that allows to alleviate the usual naturalness and coincidence problems and, on the other hand, the electromagnetic field is shown to give rise to an effective cosmological constant on large scales whose value can be explained in terms of inflation at the electroweak scale.Comment: 4 pages, 1 table. Contribution to the proceedings of Spanish Relativity Meeting 2009, Bilbao, Spain, 7-11 September 200

Cosmic magnetic fields and dark energy in extended electromagnetism

We discuss an extended version of electromagnetism in which the usual gauge fixing term is promoted into a physical contribution that introduces a new scalar state in the theory. This new state can be generated from vacuum quantum fluctuations during an inflationary era and, on super-Hubble scales, gives rise to an effective cosmological constant. The value of such a cosmological constant coincides with the one inferred from observations as long as inflation took place at the electroweak scale. On the other hand, the new state also generates an effective electric charge density on sub-Hubble scales that produces both vorticity and magnetic fields with coherent lengths as large as the present Hubble horizon.Comment: 4 pages, 2 figures. Contribution to the proceedings of Spanish Relativity Meeting 2010, Granada, Spain, 6-10 September 201

Metastability of non-reversible mean-field Potts model with three spins

We examine a non-reversible, mean-field Potts model with three spins on a set with $N\uparrow\infty$ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields. We illustrate the case of large external fields with some phenomena which are not present in the absence of external field.Comment: 34 pages, 12 figure

A cosmic vector for dark energy

In this work we show that the presence of a vector field on cosmological scales could explain the present phase of accelerated expansion of the universe. The proposed theory contains no dimensional parameters nor potential terms and does not require unnatural initial conditions in the early universe, thus avoiding the so called cosmic coincidence problem. In addition, it fits the data from high-redshift supernovae with excellent precision, making definite predictions for cosmological parameters. Upcoming observations will be able to clearly discriminate this model from standard cosmology with cosmological constant.Comment: 5 pages, 3 figures, 1 table. New comments and references included. Final version to appear in Phys. Rev.

Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case

We consider the minimal discrete and continuous energy problems on the unit sphere $\mathbb{S}^d$ in the Euclidean space $\mathbb{R}^{d+1}$ in the presence of an external field due to finitely many localized charge distributions on $\mathbb{S}^d$, where the energy arises from the Riesz potential $1/r^s$ ($r$ is the Euclidean distance) for the critical Riesz parameter $s = d - 2$ if $d \geq 3$ and the logarithmic potential $\log(1/r)$ if $d = 2$. Individually, a localized charge distribution is either a point charge or assumed to be rotationally symmetric. The extremal measure solving the continuous external field problem for weak fields is shown to be the uniform measure on the sphere but restricted to the exterior of spherical caps surrounding the localized charge distributions. The radii are determined by the relative strengths of the generating charges. Furthermore, we show that the minimal energy points solving the related discrete external field problem are confined to this support. For $d-2\leq s<d$, we show that for point sources on the sphere, the equilibrium measure has support in the complement of the union of specified spherical caps about the sources. Numerical examples are provided to illustrate our results.Comment: 23 pages, 4 figure

Minimización global de un polinomio en la recta real

En este art´ıculo presentamos y probamos num´ericamente un nuevo algoritmo para la minimizaci´on global de un polinomio de grado par. El algoritmo est´a basado en la simple idea de trasladar verticalmente el grafo del polinomio hasta que el eje OX sea tangente al grafo del polinomio trasladado. En esta privilegiada posici´on, cualquier ra´ız real del polinomio trasladado es un m´ınimo global del polinomio original