Remarks on Higgs inflation

We discuss models where the Higgs boson of the electroweak standard model plays the role of the inflaton. We focus on the question of the violation of perturbative unitarity due to the coupling of the Higgs boson either to the Ricci scalar or to the Einstein tensor and discuss the background dependence of the unitarity bounds. Our conclusion is that the simplest model which restricts itself to the standard model Higgs boson without introducing further degrees of freedom has a serious problem. However, in the asymptotically safe gravity scenario, the Higgs boson of the standard model could be the inflaton and no physics beyond the standard model is required to explain both inflation and the spontaneous breaking of the electroweak symmetry of the standard model.     

Remarks on Higgs mechanism for gravitons

We construct two kinds of model exhibiting Higgs mechanism for gravitons in potentials of scalar fields. One class of the model is based on a potential which is a generic function of the induced internal metric HAB$H^{AB}$, and the other involves a potential which is a generic function of the usual metric tensor g_μν$g_{\mu \nu }$ and the induced curved metric Y_μν$Y_{\mu \nu }$. In the both models, we derive conditions on the scalar potential in such a way that gravitons acquire mass in a flat Minkowski space–time without non-unitary propagating modes in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. We solve the conditions and find a general solution for the potential. As an interesting specific solution, we present a simple potential for which the Higgs mechanism for gravitons holds in any value of cosmological constant.     

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field φ plays in Brans–Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans–Dicke theory, we propose a new gravity theory with a complex scalar field ϕ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.     

Some Remarks on Kite Pseudo Effect Algebras

Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ,ρ:I→I. Using a clever construction on the ordinal sum of (G ⁺) ^I and (G ^?) ^I , we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.     

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.     

Some Remarks on Exp-Function Method and Its Applications

Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.     

Some Remarks on Variational Formulations of Physical Fields

A correct variational formulation of the Dirac field and some vector fields including electromagnetic field is presented based on analysis of the Dirac field equation in terms of real functions.     

Some Remarks on Large-Time Asymptotic of the Lifshitz–Slyozov Equations

We obtain an entropy functional for the Lifshitz–Slyozov system. This can be used to investigate the time asymptotics of the system. In particular, we describe situations in which the monomers concentration either tend to 0 or saturate as time becomes large. The latter situation can be excluded under assumptions on the support of the initial data.     

Some Remarks on Exp-Function Method and Its Applications-A Supplement

Recently, the authors of [Commun. Theor. Phys. 56 (2011) 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function method.     

The Common Origin of the Cosmological Constant and the Higgs Mechanism

The author’s 1997 cosmological model predicted a Dark Energy driven accelerating universe with a small cosmological constant. This was observed the very next year in a study of Type Ia supernovae. Following this work, we now deduce a value of the cosmological constant consistent with observation, and indeed the earlier work. We also argue that these considerations are also at the root of the Higgs Mechanism.     

Some Remarks on Exp-Function Method and Its Applications-A Supplement

Recently, the authors of [Commun. Theor. Phys. 56 （2011） 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function method.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

Digital Optics: Some Remarks on the Accuracy of Particle Image Analysis

The article has the aim to investigate some typical errors which arise in digital images of particles, and where it is possible, tries to assess the effective inaccuracies in the determination of distributions of size, length, perimeter and shape. In the second chapter, the errors typical for very low pixel numbers are discussed, in the third chapter, resolution independent errors in the determination of length and perimeter are investigated. In the last chapter, the consequences for shape determination are summarised.     

Some Remarks on Symmetries and Transformation Groups in General Relativity

The motivation for this paper is the recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study. The general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail. The relationship between such Lie algebras and the ideas of Lie transformation group theory (Palais' theorems) is stated and a general theorem regarding the orbits of such symmetries is given. Finally some specific symmetries in general relativity are explored and some of their similarities and differences noted.