Scalar field description for parametric models of dark energy

We investigate theoretical and observational aspects of a time-dependent parameterization for the dark energy equation of state w(z), which is a well behaved function of the redshift z over the entire cosmological evolution, i.e., z is an element of [-1, infinity). By using a theoretical algorithm of constructing the quintes-sence potential directly from the w(z) function, we derive and discuss the general features of the resulting potential for the cases in which dark energy is separately conserved and when it is coupled to dark matter. Since the parameterization here discussed allows us to divide the parametric plane in defined regions associated to distinct classes of dark energy models, we use some of the most recent observations from type Ia supernovae, baryon acoustic oscillation peak and Cosmic Microwave Background shift parameter to check which class is observationally preferred. We show that the largest portion of the confidence contours lies into the region corresponding to a possible crossing of the so-called phantom divide line at some point of the cosmic evolution.

On the motion of particles in covariant Horava-Lifshitz gravity and the meaning of the A-field

We studied the low energy motion of particles in the general covariant. version of Horava-Lifshitz gravity proposed by Horava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Horava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newton's gravity law even in the weak gravitational field approximation. (C) 2011 Elsevier B.V All rights reserved.

Twinlike models for kinks and compactons in flat and warped spacetime

This work deals with the presence of twinlike models in scalar field theories. We show how to build distinct scalar field theories having the same extended solution, with the same energy density and linear stability. Here, however, we start from a given but generalized scalar field theory, and we construct the corresponding twin model, which also engenders generalized dynamics. We investigate how the twinlike models arise in both flat and curved spacetimes. In the curved spacetime, we consider a braneworld model with the warp factor controlling the spacetime geometry with a single extra dimension of infinite extent. In particular, we study linear stability in both flat and curved spacetimes, and in the case of curved spacetime-in both the gravity and the scalar field sectors-for the two braneworld models. DOI: 10.1103/PhysRevD.86.125021

Interactive quadrangulation with reeb atlases and connectivity textures

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user's own subjective requirements.

New cosmic accelerating scenario without dark energy

We propose an alternative, nonsingular, cosmic scenario based on gravitationally induced particle production. The model is an attempt to evade the coincidence and cosmological constant problems of the standard model (Lambda CDM) and also to connect the early and late time accelerating stages of the Universe. Our space-time emerges from a pure initial de Sitter stage thereby providing a natural solution to the horizon problem. Subsequently, due to an instability provoked by the production of massless particles, the Universe evolves smoothly to the standard radiation dominated era thereby ending the production of radiation as required by the conformal invariance. Next, the radiation becomes subdominant with the Universe entering in the cold dark matter dominated era. Finally, the negative pressure associated with the creation of cold dark matter (CCDM model) particles accelerates the expansion and drives the Universe to a final de Sitter stage. The late time cosmic expansion history of the CCDM model is exactly like in the standard Lambda CDM model; however, there is no dark energy. The model evolves between two limiting (early and late time) de Sitter regimes. All the stages are also discussed in terms of a scalar field description. This complete scenario is fully determined by two extreme energy densities, or equivalently, the associated de Sitter Hubble scales connected by rho(I)/rho(f) = (H-I/H-f)(2) similar to 10(122), a result that has no correlation with the cosmological constant problem. We also study the linear growth of matter perturbations at the final accelerating stage. It is found that the CCDM growth index can be written as a function of the Lambda growth index, gamma(Lambda) similar or equal to 6/11. In this framework, we also compare the observed growth rate of clustering with that predicted by the current CCDM model. Performing a chi(2) statistical test we show that the CCDM model provides growth rates that match sufficiently well with the observed growth rate of structure.

Exact cosmological solutions of models with an interacting dark sector

In this work we extend the first order formalism for cosmological models that present an interaction between a fermionic and a scalar field. Cosmological exact solutions describing universes filled with interacting dark energy and dark matter have been obtained. Viable cosmological solutions with an early period of decelerated expansion followed by late acceleration have been found, notably one which presents a dark matter component dominating in the past and a dark energy component dominating in the future. In another one, the dark energy alone is the responsible for both periods, similar to a Chaplygin gas case. Exclusively accelerating solutions have also been obtained.

Localizability in de Sitter space

An analogue of the Newton-Wigner position operator is defined for a massive neutral scalar field in de Sitter space. The one-particle subspace of the theory, consisting of positive-energy solutions of the Klein-Gordon equation selected by the Hadamard condition, is identified with an irreducible representation of the de Sitter group. Postulates of localizability analogous to those written by Wightman for fields in Minkowski space are formulated on it, and a unique solution is shown to exist. Representations in both the principal and the complementary series are considered. A simple expression for the time evolution of the Newton-Wigner operator is presented.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Black hole formation with an interacting vacuum energy density

We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological beta parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time, but it cannot prevent the formation of a singular point. However, the nature of the singularity depends on the value of beta. In the radiation case, a trapped surface is formed for beta <= 1/2, whereas for beta >= 1/2, a naked singularity is developed. In general, the critical value is beta = 1-2/3(1 + omega) where omega is the parameter describing the equation of state of the fluid component.

Nonanalyticity of the free energy in thermal field theory

We study, in a d-dimensional space-time, the nonanalyticity of the thermal free energy in the scalar phi(4) theory as well as in QED. We find that the infrared divergent contributions induce, when d is even, a nonanalyticity in the coupling alpha of the form (alpha)((d-1)/2) whereas when d is odd the nonanalyticity is only logarithmic.

Higher spatial derivative field theories

In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz symmetry breaking that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa-like model.

Ward identities in Lifshitz-like field theories

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z = 2 in six spatial dimensions.