Cosmological dynamics of tachyonic teleparallel dark energy

A detailed dynamical analysis of the tachyonic teleparallel dark energy model, in which a non-canonical scalar field (tachyon field) is non-minimally coupled to gravitation, is performed. It is found that, when the non-minimal coupling is ruled by a dynamically changing coefficient $\alpha\equiv f_{,\phi}/\sqrt{f}$, with $f(\phi)$ an arbitrary function of the scalar field $\phi$, the universe may experience a field-matter-dominated era "$\phi$MDE", in which it has some portions of the energy density of $\phi$ in the matter dominated era. This is the most significant difference in relation to the so-called teleparallel dark energy scenario, in which a canonical scalar field (quintessence) is non-minimally coupled to gravitation.Comment: 14 pages, 1 figure. arXiv admin note: text overlap with arXiv:1305.047

A novel teleparallel dark energy model

Although equivalent to general relativity, teleparallel gravity is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the "vector torsion". This type of coupling is motivated by the fact that a scalar field couples to torsion through its four-derivative, which is consistent with local spacetime kinematics regulated by the de Sitter group $SO(1,4)$. It is found that the current state of accelerated expansion of the Universe corresponds to a late-time attractor that can be (i) a dark-energy-dominated de Sitter solution ($\omega_{\phi}=-1$), (ii) a quintessence-type solution with $\omega_{\phi}\geq-1$, or (iii) a phantom-type $\omega_{\phi}<-1$ dark energy.Comment: 15 pages, 2 figures, 3 table

Violation of causality in f(T)f(T) gravity

[Abridged] In its standard formulation, the $f(T)$ field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. A locally Lorentz covariant $f(T)$ gravity theory has been devised recently, and this local causality problem has been overcome. The nonlocal question, however, is left open. If gravitation is to be described by this covariant $f(T)$ gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous G\"odel-type solutions, which necessarily leads to violation of causality on nonlocal scale. Here, to look into the potentialities and difficulties of the covariant $f(T)$ theories, we examine whether they admit G\"odel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general G\"odel-type solution, which contains special solutions in which the essential parameter of G\"odel-type geometries, $m^2$, defines any class of homogeneous G\"odel-type geometries. We extended to the context of covariant $f(T)$ gravity a theorem, which ensures that any perfect-fluid homogeneous G\"odel-type solution defines the same set of G\"odel tetrads $h_A^{~\mu}$ up to a Lorentz transformation. We also shown that the single massless scalar field generates G\"odel-type solution with no closed timelike curves. Even though the covariant $f(T)$ gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the G\"odel-type solutions makes apparent that the covariant formulation of $f(T)$ gravity does not preclude non-local violation of causality in the form of closed timelike curves.Comment: 10 pages, V2: Presentation of Sec.2 improved, references added, version published in Eur.Phys.J.

Social Housing under Oligopoly

In this paper it is shown that the setting up of a social housing system may decrease the total number of houses built in the market, induce a price of non-social houses greater than the price of houses without that system and increase the profits of housing developers even in situations where they have to sell social houses at a price below production cost. The analysis considers a situation with imperfect competition in the housing market and with a social housing system where housing developers must provide some social houses when they obtain a permit to build non-social houses.social housing, imperfect competition, housing stock

Non-Stationary Demand in a Durable Goods Monopoly

In a context where demand for the services of a durable good changes over time, and this change may be uncertain, the paper shows that social welfare may be higher when the monopolist seller can commit to any future price level she wishes than when she cannot. Moreover, the equilibrium under a monopolist with commitment power may Pareto-dominate the equilibrium under a monopolist without commitment ability. These results affect the desired regulation of a durable goods monopolist in this context.commitment, demand variations, regulation, durable goods

Commitment Power in a Non-Stationary Durable-Good Market

This paper derives and evaluates the decisions of a durable good monopolist in a context where demand for the services of the durable good changes over time. It shows that, if the size of the market decreases over time, social welfare may be higher when the monopolist has commitment ability than when she has not. Moreover, the equilibrium under a monopolist seller with commitment power may Pareto-dominate the equilibrium under a monopolist seller without commitment ability. The work also proves that these results obtain if there is uncertainty about future demand for the services of the durable good.commitment ability, demand variations, monopoly, durable goods

Conformal and gauge invariant spin-2 field equations

Using an approach based on the Casimir operators of the de Sitter group, the conformal invariant equations for a fundamental spin-2 field are obtained, and their consistency discussed. It is shown that, only when the spin-2 field is interpreted as a 1-form assuming values in the Lie algebra of the translation group, rather than a symmetric second-rank tensor, the field equation is both conformal and gauge invariant.Comment: 12 pages, no figures; accepted for publication in Gravitation & Cosmolog