Cuscuton: A Causal Field Theory with an Infinite Speed of Sound

We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a non-canonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces are the family of Constant Mean Curvature (CMC) hypersurfaces, which are the analogs of soap films (or soap bubbles) in a Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski spacetime, a companion paper (astro-ph/0702002) examines cosmology with Cuscuton dark energy.Comment: 11 pages, 1 figure, added discussion of "coupled cuscuton", matches the published version in PR

Rewriting Constraint Models with Metamodels

An important challenge in constraint programming is to rewrite constraint models into executable programs calculat- ing the solutions. This phase of constraint processing may require translations between constraint programming lan- guages, transformations of constraint representations, model optimizations, and tuning of solving strategies. In this paper, we introduce a pivot metamodel describing the common fea- tures of constraint models including different kinds of con- straints, statements like conditionals and loops, and other first-class elements like object classes and predicates. This metamodel is general enough to cope with the constructions of many languages, from object-oriented modeling languages to logic languages, but it is independent from them. The rewriting operations manipulate metamodel instances apart from languages. As a consequence, the rewriting operations apply whatever languages are selected and they are able to manage model semantic information. A bridge is created between the metamodel space and languages using parsing techniques. Tools from the software engineering world can be useful to implement this framework

A de Sitter limit analysis for dark energy and modified gravity models

The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behaviour of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the St\"uckelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameters space identified by requiring no-ghost instabilities and positive squared speeds of propagation does not change by performing a field redefinition, while the requirement of the avoidance of tachyonic instability might instead be different. Therefore, we find interesting to associate to the general modified gravity theory described in the effective field theory framework, a perturbation field which will inherit the whole properties of the theory. In the present paper we address the following questions: 1) how can we define such a field? and 2) what is the mass of such a field as the background approaches a final de Sitter state? We define a gauge invariant quantity which identifies the density of the dark energy perturbation field valid for any background. We derive the mass associated to the gauge invariant dark energy field on a de Sitter background, which we retain to be still a good approximation also at very low redshift ($z\simeq 0$). On this background we also investigate the value of the speed of propagation and we find that there exist classes of theories which admit a non-vanishing speed of propagation, even among the Horndeski model, for which in literature it has previously been found a zero speed. We finally apply our results to specific well known models.Comment: 22 page

Gravitational collapse of k-essence

We perform numerical simulations of the gravitational collapse of a k-essence scalar field. When the field is sufficiently strongly gravitating, a black hole forms. However, the black hole has two horizons: a light horizon (the ordinary black hole horizon) and a sound horizon that traps k-essence. In certain cases the k-essence signals can travel faster than light and the sound horizon is inside the light horizon. Under those circumstances, k-essence signals can escape from the black hole. Eventually, the two horizons merge and the k-essence signals can no longer escape.Comment: 14 pages, 8 figure

(Co-)Inductive semantics for Constraint Handling Rules

In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over the transition system generated by the abstract operational semantics of CHR. Similarly, we demonstrate that the logical reading of states with respect to a set of propagation rules can be characterized by a greatest fixpoint. Then, in order to take advantage of both types of rules without losing fixpoint characterization, we present an operational semantics with persistent. We finally establish that this semantics can be characterized by two nested fixpoints, and we show the resulting language is an elegant framework to program using coinductive reasoning.Comment: 17 page