The nature of the initial singularity

We consider the initial singularity in the universe as isotropic and with a strength the same as that of the singularity in the density function. We consider the effect of this initial singularity on a particle falling into it in the future at a high speed. This gives a precise understanding of the fate of particles falling into the final singularity in the future of aK=+1 Friedmann-Le Maitre-Robertson-Walker universe.     

On vacuum density,the initial singularity and dark energy

Standard cosmology poses a number of important questions. Apart from its singular origin, it possesses early and late accelerating phases required to account for observations. The vacuum energy has been considered as a possible way to resolve some of these questions. The vacuum energy density induced by free fields in an early de Sitter phase has earlier been estimated to be proportional to H ⁴, while more recently it has been suggested that the QCD condensate induces a term proportional to H at late times. These results have been employed in models which are non-singular and inflationary at early times and accelerating at late times. Here we cast these models in terms of scalar fields and study the corresponding spectrum of primordial perturbations. At early times the spectrum is found to be not scale-invariant, thus implying that slow-roll inflation is still required after the phase transition induced by the vacuum. At late times the corresponding scalar-field potential is harmonic, with a mass of the order of the Hubble scale, a result that may be understood in the light of the holographic conjecture.     

On the initial singularity in the scalar-tensor anisotropic cosmology

In connection with the problem of the initial singularity in the scalar-tensor anisotropic cosmology of Jordan-Brans-Dicke, the dynamics of homogeneous models of Bianchi type I is examined on the basis of the general analytic solutions in vacuo and in the presence of gravitating matter with state equations P=n? (0 ? n ? 1). It is shown that the scalar homogeneous ?-field, as an effective source of the V₄geometry, has to influence essentially the dynamics of the early anisotropic stage of the Universe's expansion, and significantly modifies the character of the initial singularity. At negative ω (ω < ?6), the sourceless scalar ?-field may remove the singularity and provide regular ‘bouncing’ in the models with matter (P ? ?/3) if it prevails over the tensor anisotropic mode of the vacuum gravitational field.     

Using Energy Conditions to Distinguish Brane Models and Study Brane Matter

Current universe (assumed here to be normal matter on the brane) is pressureless from observations. In this case the energy condition is ρ₀≥0 and p₀=0. By using this condition, brane models can be distinguished. Then, assuming arbitrary component of matter in DGP model, we use four known energy conditions to study the matter on the brane. If there is nonnormal matter or energy (for example dark energy with w<-1/3) on the brane, the universe is accelerated.     

Using Energy Conditions to Distinguish Brane Models and Study Brane Matter

Current universe （assumed here to be normal matter on the brahe） is pressureless from observations. In this case the energy condition is po ≥ 0 and po =O. By using this condition, brahe models can be distinguished. Then, assuming arbitrary component of matter in DGP model, we use four known energy conditions to study the matter on the brahe. If there is nonnormal matter or energy （for example dark energy with w 〈-1/3） on the brane, the universe is accelerated.     

The behavior of the gravitational field near the initial singularity

The ultralocal representation of the canonically quantized gravitational field is used to obtain the evolution of coherent states in the immediate neighborhood of the singularity. It is shown that smearing functions play the role of classical fields since they correspond to cosmological solutions around the singularity. A special class of ultralocal coherent states is shown to contain the essential aspects of the dynamics of the system when we choose a simple representation for the field operators of the theory. When the ultralocality condition is broken a conjecture will be made about the quantum evolution of coherent states in the classical limit.     

The dynamical behavior of scalar fields near the initial singularity

Analyzing the Klein-Gordon equation in a homogeneous, Isotropic and spatially flat universe model, we find the conditions for the existence of a universe dominated by a scalar field in its early stages.     

Brane tilings and reflexive polygons

Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories of D3 branes with toric Calabi‐Yau moduli spaces that are conveniently described with brane tilings. We find all 30 theories corresponding to the 16 reflexive polygons, some of the theories being toric (Seiberg) dual to each other. The mesonic generators of the moduli spaces are identified through the Hilbert series. It is shown that the lattice of generators is the dual reflexive polygon of the toric diagram. Thus, the duality forms pairs of quiver gauge theories with the lattice of generators being the toric diagram of the dual and vice versa.     

Brane tilings and their applications

We review recent developments in the theory of brane tilings and four‐dimensional 𝒩 = 1 supersymmetric quiver gauge theories. This review consists of two parts. In part I, we describe foundations of brane tilings, emphasizing the physical interpretation of brane tilings as fivebrane systems. In part II, we discuss application of brane tilings to AdS/CFT correspondence and homological mirror symmetry. More topics, such as orientifold of brane tilings, phenomenological model building, similarities with BPS solitons in supersymmetric gauge theories, are also briefly discussed. This paper is a revised version of the author's master's thesis submitted to Department of Physics, Faculty of Science, the University of Tokyo on January 2008, and is based on his several papers and some works in progress [1–7].     

Shearograms of an optical phase singularity

Shearograms are known to represent phase gradients but when vortices are present in the optical field, these do not represent true phase gradients. Phase gradients of an optical phase singularity are presented. A lateral shear interferometer is used for obtaining shearograms of optical fields with vortices. A diffractive phase element is used to generate vortices. It is shown that shearograms can be used in the detection of optical vortices. Shearogram of speckle field is also presented.     

Simultaneous vibrational relaxation and radiative decay of initial Boltzmann distributions

Exact solutions for the probabilities of occupation of the states of a harmonic oscillator undergoing simultaneous (vibrational) relaxation and (radiative) decay are obtained for initial Boltzmann distributions and it is shown that they maintain their Boltzmann form throughout the process.     

Fast initial decay of molecular excitations at insulator surfaces

We investigate the initial decay of electron-hole excitations in a molecular layer after adsorption on an insulator substrate surface. This is done within ab initio many-body perturbation theory by calculating the time propagation of excited two-particle states. For a CO monolayer adsorbed on the MgO(001) surface we find very fast decay processes with lifetimes that are about 5 times shorter than the transfer of single charge carriers. This is due to a strong coupling of the molecular excitations to charge-transfer-exciton states between the adlayer and the substrate.     

Spherically Symmetric Vacuum Brane and Wormhole Solutions

In this letter, we have obtained static, spherically symmetric solutions of the effective vacuum Einstein field equations on a brane embedded in a five dimensional space time. The effective stress tensor is induced by the interaction with the bulk gravitational field and is given by the electric part of the five dimensional Weyl tensor. Due to traceless nature of this non-local effect of the bulk, any solution of  ⁽⁴⁾ R=0 is a possible solution of the vacuum brane. We have derived a class of solutions, which corresponds to wormhole solution. Physical properties and characteristics of the wormhole are studied.     

A scalar polynomial singularity without an event horizon

It is shown that the solution of the field equations for a static spherically symmetric scalar field has a scalar polynomial singularity and no event horizon. The solution does not develop from nonsingular data on any Cauchy surface. The possible existence of a universal scalar field, the conformal diagram and geodesies of the solution, and the energy and momentum of the field present are discussed.