scholarly journals Testing an Inflation Model with Nonminimal Derivative Coupling in the Light of Planck 2015 Data

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Kourosh Nozari ◽  
Narges Rashidi
Keyword(s):  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Inflationary Model ◽  
Third Order ◽  
Derivative Coupling ◽  
Planck Data ◽  
The Third ◽  
Inflation Model ◽  
Complete Treatment ◽  
Point Correlation

We study the dynamics of a generalized inflationary model in which both the scalar field and its derivatives are coupled with the gravity. We consider a general form of the nonminimal derivative coupling in order to have a complete treatment of the model. By expanding the action up to the second order in perturbation, we study the spectrum of the primordial modes of the perturbations. Also, by expanding the action up to the third order and considering the three-point correlation functions, the amplitude of the non-Gaussianity of the primordial perturbations is studied in both equilateral and orthogonal configurations. Finally, by adopting some sort of potentials, we compare the model in hand with the Planck 2015 released observational data and obtain some constraints on the model’s parameters space. As an important result, we show that the nonminimal couplings help to make models of chaotic inflation that would otherwise be in tension with Planck data, in better agreement with the data. This model is consistent with observation at weak coupling limit.

scholarly journals More on the Non-Gaussianity of Perturbations in a Nonminimal Inflationary Model

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
R. Shojaee ◽  
K. Nozari ◽  
F. Darabi
Keyword(s):  
Scalar Field ◽  
Observational Data ◽  
Coupling Parameter ◽  
Extended Model ◽  
Inflationary Model ◽  
Cosmological Perturbations ◽  
Third Order ◽  
The Third ◽  
Non Gaussian

We study nonlinear cosmological perturbations and their possible non-Gaussian character in an extended nonminimal inflation where gravity is coupled nonminimally to both the scalar field and its derivatives. By expansion of the action up to the third order, we focus on the nonlinearity and non-Gaussianity of perturbations in comparison with recent observational data. By adopting an inflation potential of the form V(ϕ)=1/nλϕn, we show that, for n=4, for instance, this extended model is consistent with observation if 0.013<λ<0.095 in appropriate units. By restricting the equilateral amplitude of non-Gaussianity to the observationally viable values, the coupling parameter λ is constrained to the values λ<0.1.

scholarly journals On three new principles in non-equilibrium statistical mechanics and Markov semigroups of weak coupling limit type

2016 ◽  
Vol 19 (02) ◽  
pp. 1650009 ◽  
Author(s):  
Luigi Accardi ◽  
Franco Fagnola ◽  
Roberto Quezada
Keyword(s):  
Statistical Mechanics ◽  
Master Equation ◽  
Weak Coupling ◽  
Detailed Balance ◽  
Weak Coupling Limit ◽  
Markov Semigroups ◽  
Equilibrium Statistical Mechanics ◽  
Equation Formulation ◽  
The Third ◽  
Kms Condition

We introduce three new principles: the nonlinear Boltzmann–Gibbs prescription, the local KMS condition and the generalized detailed balance (GDB) condition. We prove the equivalence of the first two under general conditions and we discuss a master equation formulation of the third one.

scholarly journals Bounds on the Effective Transport and Elastic Properties of a Random Array of Cylindrical Fibers in a Matrix

1988 ◽  
Vol 55 (2) ◽  
pp. 347-354 ◽  
Author(s):  
S. Torquato ◽  
F. Lado
Keyword(s):  
Correlation Function ◽  
Upper And Lower Bounds ◽  
Third Order ◽  
Volume Fractions ◽  
The Third ◽  
Plastic Composite ◽  
Wide Range ◽  
Effective Transport ◽  
Point Correlation ◽  
Point Correlation Function

This paper studies the determination of rigorous upper and lower bounds on the effective transport and elastic moduli of a transversely isotropic fiber-reinforced composite derived by Silnutzer and by Milton. The third-order Silnutzer bounds on the transverse conductivity σe, the transverse bulk modulus ke, and the axial shear modulus μe, depend upon the microstructure through a three-point correlation function of the medium. The fourth-order Milton bounds on σe and μe depend not only upon three-point information but upon the next level of information, i.e., a four-point correlation function. The aforementioned microstructure-sensitive bounds are computed, using methods and results of statistical mechanics, for the model of aligned, infinitely long, equisized, circular cylinders which are randomly distributed throughout a matrix, for fiber volume fractions up to 65 percent. For a wide range of volume fractions and phase property values, the Silnutzer bounds significantly improve upon corresponding second-order bounds due to Hill and to Hashin; the Milton bounds, moreover, are narrower than the third-order Silnutzer bounds. When the cylinders are perfectly conducting or perfectly rigid, it is shown that Milton’s lower bound on σe or μe provides an excellent estimate of these effective parameters for the wide range of volume fractions studied here. This conclusion is supported by computer-simulation results for σe and by experimental data for a graphite-plastic composite.

scholarly journals On the order reduction

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Waleska P. F. de Medeiros ◽  
Daniel Müller
Keyword(s):  
Exact Solutions ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Order Reduction ◽  
Weak Coupling Limit ◽  
Reduction Technique ◽  
Inflationary Model ◽  
Iterative Technique ◽  
Realistic Case ◽  
Slow Roll

AbstractIn this work we present an extension of the technique of the order reduction to higher perturbative approximations in an iterative fashion. The intention is also to analyze more carefully the conditions for the validity of the order reduction technique. With this in mind, a few simple situations in which the iterative order reduction converges analytically to the exact solutions are presented as examples. It is discovered that the order reduction as a perturbative iterative technique does not converge in the weak coupling limit as most of the known perturbative schemes, at least when applied to these examples. Also, considering these specific examples, the convergence of the order reduction occurs in strong coupling regimes. As a more realistic case, the order reduction is applied to Starobinsky’s inflationary model is presented. It is verified that the method converges to the inflationary solution in the slow-roll regime.

scholarly journals Semiclassical analysis of the tensor power spectrum in the Starobinsky inflationary model

2021 ◽  
pp. 2150040
Author(s):  
Truman Tapia ◽  
Clara Rojas
Keyword(s):  
Power Spectrum ◽  
Approximation Method ◽  
Uniform Approximation ◽  
Integral Method ◽  
Inflationary Model ◽  
Semiclassical Analysis ◽  
Third Order ◽  
Tensor Power ◽  
The Third ◽  
Slow Roll

In this work, we calculate the tensor power spectrum and the tensor-to-scalar ratio [Formula: see text] within the frame of the Starobinsky inflationary model using the improved uniform approximation method and the third-order phase-integral method. We compare our results with those obtained with numerical integration and the slow-roll approximation to second-order. We have obtained consistent values of [Formula: see text] using the different approximations, and [Formula: see text] is inside the interval reported by observations.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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