Spectra in Coherent States with Excited-de Sitter Mode during Inflation

We use an excited-de Sitter mode as the fundamental mode function for the far past time limit during inflation, to study the corrections of spectra of curvature perturbation. Excited-de Sitter mode is actually the approximate solution of the inflaton field equation that asymptotically approaches to the de Sitter mode function in the first approximation. We build coherent state over excited-de Sitter mode. Then, we compute spectrum of the curvature perturbation with this coherent state as the initial state. We show that in this case, the spectrum of curvature perturbation is scale dependent. As a important result of using this coherent state, we find a non-zero non-Gaussian one-point function as a possible tiny source for generation of anisotropy in CMB from the initial mode in the string or Planck scale.     

Design of a cyclic multiverse

Recently, it has been noticed that the amplification of the amplitude of curvature perturbation cycle by cycle can lead to a cyclic multiverse scenario, in which the number of universes increases cycle by cycle. However, this amplification will also inevitably induce either the ultimate end of corresponding cycle, or the resulting spectrum of perturbations inside corresponding universe is not scale invariant, which baffles the existence of observable universes. In this Letter, we propose a design of a cyclic multiverse, in which the observable universe can emerges naturally. The significance of a long period of dark energy before the turnaround of each cycle for this implementing is shown.     

On the finiteness of a new topological model in D=3

A new topological model is proposed in three dimensions as an extension of the BF-model. It is a three-dimensional counterpart of the two-dimensional model introduced by Chamseddine and Wyler ten years ago. The BFK-model, as we shall call it, shows to be quantum scale invariant at all orders in perturbation theory. The proof of its full finiteness is given in the framework of algebraic renormalization.     

Canonical Sasakian Metrics

Let M be a closed manifold of Sasaki type. A polarization of M is defined by a Reeb vector field, and for any such polarization, we consider the set of all Sasakian metrics compatible with it. On this space we study the functional given by the square of the L ²-norm of the scalar curvature. We prove that its critical points, or canonical representatives of the polarization, are Sasakian metrics that are transversally extremal. We define a Sasaki-Futaki invariant of the polarization, and show that it obstructs the existence of constant scalar curvature representatives. For a fixed CR structure of Sasaki type, we define the Sasaki cone of structures compatible with this underlying CR structure, and prove that the set of polarizations in it that admit a canonical representative is open. We use our results to describe fully the case of the sphere with its standard CR structure, showing that each element of its Sasaki cone can be represented by a canonical metric; we compute their Sasaki-Futaki invariant, and use it to describe the canonical metrics that have constant scalar curvature, and to prove that only the standard polarization can be represented by a Sasaki-Einstein metric. During the preparation of this work, the first two authors were partially supported by NSF grant DMS-0504367.     

Reheating in tachyonic inflationary models: Effects on the large scale curvature perturbations

We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch on the evolution of the large scale curvature and non-adiabatic pressure perturbations. We consider two different potentials to describe the tachyon and study the effects of two possible types of decay of the tachyon into radiation. We plot the spectrum of curvature perturbations at the end of inflation as well as at the early stages of the radiation dominated epoch. We find that reheating does not affect the amplitude of the curvature perturbations in any of these cases. These results corroborate similar conclusions that have been arrived at earlier based on the study of the evolution of the perturbations in the super-Hubble limit. We illustrate that, before the transition to the radiation dominated epoch, the relative non-adiabatic pressure perturbation between the tachyon and radiation decays in a fashion very similar to that of the intrinsic entropy perturbation associated with the tachyon. Moreover, we show that, after the transition, the relative non-adiabatic pressure perturbation dies down extremely rapidly during the early stages of the radiation dominated epoch. It is these behavior which ensure that the amplitude of the curvature perturbations remain unaffected during reheating. We also discuss the corresponding results for the popular chaotic inflation model in the case of the canonical scalar field.     

Effects of a decaying cosmological fluctuation

We present the initial conditions for a decaying cosmological perturbation and study its signatures in the cosmic microwave background anisotropies and matter power spectra. An adiabatic decaying mode in the presence of components that are not described as perfect fluids (such as collisionless matter) decays slower than in a perfect-fluid dominated Universe and displays super-Hubble oscillations. Wilkinson Microwave Anisotropy Probe first year data constrain the decaying to growing ratio of scale invariant adiabatic fluctuations at the matter-radiation equality to less than 10%.     

Emergent universe from scale invariant two measures theory

The dilaton-gravity sector of a linear in the scalar curvature, scale invariant Two Measures Field Theory (TMT), is explored in detail in the context of closed FRW cosmology and shown to allow stable emerging universe solutions. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. We study the transition from the emerging phase to inflation, and then to a zero cosmological constant phase. We also study the spectrum of density perturbations and the constraints that impose on the parameters of the theory.     

Local and non-local curvature approximation: a new asymptotic theory for wave scattering

Abstract

We present a new asymptotic theory for scalar and vector wave scattering from rough surfaces which federates an extended Kirchhoff approximation (EKA), such as the integral equation method (IEM), with the first and second order small slope approximations (SSA). The new development stems from the fact that any improvement of the ‘high frequency’ Kirchhoff or tangent plane approximation (KA) must come through surface curvature and higher order derivatives. Hence, this condition requires that the second order kernel be quadratic in its lowest order with respect to its Fourier variable or formally the gradient operator. A second important constraint which must be met is that both the Kirchhoff approximation (KA) and the first order small perturbation method (SPM-1 or Bragg) be dynamically reached, depending on the surface conditions. We derive herein this new kernel from a formal inclusion of the derivative operator in the difference between the polarization coefficients of KA and SPM-1. This new kernel is as simple as the expressions for both Kirchhoff and SPM-1 coefficients. This formal difference has the same curvature order as SSA-1 + SSA-2. It is acknowledged that even though the second order small perturbation method (SPM-2) is not enforced, as opposed to the SSA, our model should reproduce a reasonable approximation of the SPM-2 function at least up to the curvature or quadratic order. We provide three different versions of this new asymptotic theory under the local, non-local, and weighted curvature approximations. Each of these three models is demonstrated to be tilt invariant through first order in the tilting vector.     

Primordial curvature perturbation during and at the end of multi-field inflation

We study the generation of the primordial curvature perturbation in multi-field inflation. Considering both the evolution of the perturbation during inflation and the effects generated at the end of inflation, we present a general formula for the curvature perturbation. We provide the analytic expressions of the power spectrum, spectral tilt and non-Gaussianity for the separable potentials of two inflaton scalars, and apply them to some specific models.     

G-Curvaton

In this Letter, we study a curvaton model where the curvaton is acted by Galileon field. We calculate the power spectrum of fluctuation of G-Curvaton during inflation and discuss how it converts to the curvature perturbation after the end of inflation. We estimate the bispectrum of curvature perturbation induced, and show the dependence of non-Gaussianity on the parameters of model. It is found that our model can have sizable local and equilateral non-Gaussianities to up to O(¹⁰²), which is illustrated by an explicit example.     

Modular thermal inflation without slow-roll approximation

We study an inflationary scenario where thermal inflation is followed by fast-roll inflation. This is a rather generic possibility based on the effective potentials of spontaneous symmetry breaking in the context of particle physics models. We show that a large enough expansion could be achieved to solve cosmological problems. However, the power spectrum of primordial density perturbations from the quantum fluctuations in the inflaton field is not scale invariant and thus inconsistent with observations. Using the curvaton mechanism instead, we can obtain a nearly scale invariant spectrum, provided that the inflationary energy scale is sufficiently low to have long enough fast-roll inflation to dilute the perturbations produced by the inflaton fluctuations.     

A Galileon design of slow expansion: Emergent universe

We parameterize the evolutions of the slow expansion, which emerges from a static state in infinite past, into different classes. We show that the scale invariant adiabatical perturbation may be generated during these evolutions, and the corresponding evolutions can be realized with generalized Galileon Lagrangians, in which there is not the ghost instability.     

Non-Hermitian Kitaev chain with complex periodic and quasiperiodic potentials

We study the topological properties of the one-dimensional non-Hermitian Kitaev model with complex either periodic or quasiperiodic potentials. We obtain the energy spectrum and the phase diagrams of the system by using the transfer matrix method as well as the topological invariant. The phase transition points are given analytically. The Majorana zero modes in the topological nontrivial regimes are obtained. Focusing on the quasiperiodic potential, we obtain the phase transition from the topological superconducting phase to the Anderson localization, which is accompanied with the Anderson localization–delocalization transition in this non-Hermitian system. We also find that the topological regime can be reduced by increasing the non-Hermiticity.     

Perturbation of Symmetries and Hojman Adiabatic Invariants for Mechanical Systems with Unilateral Holonomic Constraints

The perturbation of symmetries and adiabatic invariants for mechanical systems with unilateral holonomic constraints are studied. The exact invariant in the form of Hojman led by special Lie symmetries for an undisturbed system with unilateral constraints is given. Based on the concept of high-order adiabatic invariant of mechanical systems, the perturbation of Lie symmetries for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the system with unilateral holonomic constraints is obtained, which can be called Hojman adiabatic invariant. In the end of the paper, an example is given to illustrate the application of the results.     

Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space

For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results.     

Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures.

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.     

Black hole spectroscopy via adiabatic invariance

During the last years, one had to combine the proposal about how quasinormal frequencies are related with black holes and the proposal about the adiabatic invariance of black holes in order to derive the quantized entropy spectrum and its minimum change for several black holes. In this Letter we exclusively utilize the statement that the black hole horizon area is an adiabatic invariant and derive an equally spaced entropy spectrum of a black hole with its quantum to be equal to the one given by Bekenstein. Interestingly, in our approach no concept of quasi-normal mode is needed.     

Reexamination of the power spectrum in de Sitter inflation

We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.     

Possibility of observable amount of gravitational waves from inflation

The curvaton and inhomogeneous reheating scenarios for the generation of the cosmological curvature perturbation on large scales represent an alternative to the standard slow-roll scenario. The basic assumption of these mechanisms is that the initial curvature perturbation due to the inflaton field is negligible. This is usually attained by lowering the energy scale of inflation, thereby concluding that the amount of gravitational waves produced during inflation is highly suppressed. We show that the curvaton and inhomogeneous reheating scenarios are compatible with a level of gravity-wave fluctuations which may well be observed in future satellite experiments.     

Controllable soliton propagation based on phase-front curvature in asymmetrical nonlocal media

The influence of phase-front curvature on the dynamical behavior of the fundamental mode soliton during its transmission in asymmetrical nonlocal media is studied in detail and the phase-front curvature can be imposed on the fundamental mode soliton by reshaping or phase imprinting technologies. By changing the phase-front curvature or its imposed position,controllable soliton propagation in asymmetrical nonlocal media can be achieved.