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 Spin-locality of η2 and $$ {\overline{\eta}}^2 $$ quartic higher-spin vertices

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
V. E. Didenko ◽  
O. A. Gelfond ◽  
A. V. Korybut ◽  
M. A. Vasiliev
Keyword(s):  
Scalar Field ◽  
Coupling Parameter ◽  
Complex Conjugate ◽  
Third Order ◽  
The Third ◽  
Order Contribution ◽  
Higher Spin ◽  
Higher Spin Theory

Abstract Higher-spin theory contains a complex coupling parameter η. Different higher-spin vertices are associated with different powers of η and its complex conjugate $$ \overline{\eta} $$ η ¯ . Using Z-dominance Lemma of [1], that controls spin-locality of the higher-spin equations, we show that the third-order contribution to the zero-form B(Z; Y; K) admits a Z-dominated form that leads to spin-local vertices in the η2 and $$ {\overline{\eta}}^2 $$ η ¯ 2 sectors of the higher-spin equations. These vertices include, in particular, the η2 and $$ {\overline{\eta}}^2 $$ η ¯ 2 parts of the ϕ4 scalar field vertex.

scholarly journals First passage probability assessment of stationary non-Gaussian process using the third-order polynomial transformation

2018 ◽  
Vol 22 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Yan-Gang Zhao ◽  
Long-Wen Zhang ◽  
Zhao-Hui Lu ◽  
Jun He
Keyword(s):  
Gaussian Process ◽  
Probability Assessment ◽  
Third Order ◽  
First Passage ◽  
The Third ◽  
Polynomial Transformation ◽  
Order Polynomial ◽  
First Passage Probability ◽  
Non Gaussian ◽  
First Four Moments

In this article, an analytical moment-based procedure is developed for estimating the first passage probability of stationary non-Gaussian structural responses for practical applications. In the procedure, an improved explicit third-order polynomial transformation (fourth-moment Gaussian transformation) is proposed, and the coefficients of the third-order polynomial transformation are first determined by the first four moments (i.e. mean, standard deviation, skewness, and kurtosis) of the structural response. The inverse transformation (the equivalent Gaussian fractile) of the third-order polynomial transformation is then used to map the marginal distributions of a non-Gaussian response into the standard Gaussian distributions. Finally, the first passage probabilities can be calculated with the consideration of the effects of clumping crossings and initial conditions. The accuracy and efficiency of the proposed transformation are demonstrated through several numerical examples for both the “softening” responses (with wider tails than Gaussian distribution; for example, kurtosis > 3) and “hardening” responses (with narrower tails; for example, kurtosis < 3). It is found that the proposed method has better accuracy for estimating the first passage probabilities than the existing methods, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian process.

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 Scalar and electromagnetic quasinormal modes of an extended black hole in F(R) gravity

2015 ◽  
Vol 30 (05) ◽  
pp. 1550012 ◽  
Author(s):  
Saneesh Sebastian ◽  
V. C. Kuriakose
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Imaginary Part ◽  
Quasinormal Modes ◽  
Quasinormal Mode ◽  
Wkb Method ◽  
Third Order ◽  
Absolute Value ◽  
The Third ◽  
The Absolute

In this paper, we study the scalar and electromagnetic perturbations of an extended black hole in F(R) gravity. The quasinormal modes in two cases are evaluated and studied their behavior by plotting graphs in each case. To study the quasinormal mode, we use the third-order WKB method. The present study shows that the absolute value of imaginary part of complex quasinormal modes increases in both cases, thus the black hole is stable against these perturbations. As the mass of the scalar field increases the imaginary part of the frequency decreases. Thus, damping slows down with increasing mass of the scalar field.

scholarly journals On the anisotropy of the turbulent passive scalar in the presence of a mean scalar gradient

2014 ◽  
Vol 744 ◽  
pp. 38-64 ◽  
Author(s):  
Wouter J. T. Bos
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Time Scale ◽  
Correlation Time ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Second Order ◽  
Third Order ◽  
The Third ◽  
Order Quantities

AbstractWe investigate the origin of the scalar gradient skewness in isotropic turbulence on which a mean scalar gradient is imposed. The problem of the advection of an anisotropic scalar field is reformulated in terms of the advection of an isotropic vector field. For this field, triadic closure equations are derived. It is shown how the scaling of the scalar gradient skewness depends on the choice of the time scale used for the Lagrangian decorrelation of the vector field. The persistent anisotropy in the small scales for the third-order statistics is shown to be perfectly compatible with Corrsin–Obukhov scaling for second-order quantities, since second- and third-order scalar quantities are governed by a different triad correlation time scale. Whereas the inertial range dynamics of second-order scalar quantities is governed by the Lagrangian velocity correlation time, the third-order quantities remain correlated over a time related to the large-scale dynamics of the scalar field. It is argued that this time is determined by the average time it takes for a fluid particle to travel between ramp-cliff scalar structures.

Massive scalar field quasinormal modes of a black hole in the deformed Hořava-Lifshitz gravity

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
ChunYan Wang ◽  
YaJun Gao
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Quasinormal Modes ◽  
Massive Scalar ◽  
Coupling Constant ◽  
Field Mass ◽  
Third Order ◽  
Massive Scalar Field ◽  
The Third ◽  
Black Hole Spacetime

AbstractWe calculated the quasinormalmodes ofmassive scalar field of a black hole in the deformed Hořava-Lifshitz gravity with coupling constant λ = 1, using the third-order WKB approximation. Our results show that when the scalar field mass increases, the oscillation frequency increases while the damping decreases. And we find that the imaginary parts are almost linearly related to the real parts, the behaviors are very similar to that in the Reissner-Nordström black hole spacetime. These information will help us understand more about the Hořava-Lifshitz gravity.

Some aspects of nonminimal inflation driven by a superpotential

2016 ◽  
Vol 26 (07) ◽  
pp. 1750058
Author(s):  
Kourosh Nozari ◽  
Narges Rashidi
Keyword(s):  
Spectral Index ◽  
Second Order ◽  
Numerical Results ◽  
Nonminimal Coupling ◽  
Third Order ◽  
The Third ◽  
Scalar Spectral Index ◽  
Non Gaussian

We study a nonminimal inflation which is driven by a superpotential. By adopting the Arnowitt–Deser–Misner formalism, we explore the primordial perturbations and its non-Gaussianity in this framework. By expanding the action up to the second-order in perturbations, we seek the scalar spectral index, its running and the tensor-to-scalar ratio. In this regard, we find the ranges of the nonminimal coupling and superpotential parameters which lead to the observationally viable perturbations parameters. The non-Gaussian feature in both the equilateral and orthogonal configurations in this setup, is studied by exploring the third-order action. We show that in some ranges of the nonminimal and superpotential parameters, the model predicts large non-Gaussianity. By comparing the numerical results with Planck2015 data, we test the viability of the model and find some constraints on the model’s parameters space.

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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