On the evolution and stability of cosmological perturbations in higher order scalar–tensor theories of gravity

2019 ◽  
Vol 97 (4) ◽  
pp. 360-373
Author(s):  
Fateme Rajabi ◽  
Kourosh Nozari
Keyword(s):  
Scalar Field ◽  
Higher Order ◽  
De Sitter ◽  
Cosmological Perturbations ◽  
First Order ◽  
Higher Order Terms ◽  
General Scalar ◽  
New Type ◽  
Theories Of Gravity ◽  
The Stability

We study a new type of extended theory of gravity in the framework of general scalar–tensor theories in which the higher order terms of curvature are coupled with a scalar field and its derivatives. We analyze the stability and evolution of cosmological perturbations in this setup. For this purpose, we perturb the Hubble parameter, matter density, and scalar field to check stability and evolution of perturbations to first order. In this framework, we investigate stability conditions for de Sitter and power law solutions and we examine viability of cosmological evolution of these perturbations. We consider some specific f(R) models and show that the stability analysis gives some constraints on the parameters of these models.

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

scholarly journals CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

2012 ◽  
Vol 10 ◽  
pp. 63-68 ◽  
Author(s):  
JE-AN GU
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Early Time ◽  
Einstein Equations ◽  
Modified Theories Of Gravity ◽  
Cosmological Perturbations ◽  
Long Run ◽  
Theories Of Gravity ◽  
The Stability ◽  
Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

scholarly journals Removing Ostrogradski’s ghost from cosmological perturbations in f(R,Rμν2,Cμνρσ2) gravity

2016 ◽  
Vol 31 (11) ◽  
pp. 1650067 ◽  
Author(s):  
Yuji Akita ◽  
Tsutomu Kobayashi
Keyword(s):  
General Formula ◽  
Ricci Tensor ◽  
Matter Density ◽  
De Sitter ◽  
Cosmological Perturbations ◽  
Text Type ◽  
Cosmological Background ◽  
Density Perturbations ◽  
Sitter Background ◽  
Theories Of Gravity

Recently, it was argued that gravity with the square of the Ricci tensor can be stabilized by adding constraints to the theory in a Lorentz violating way. This was so far demonstrated for fluctuations on the Minkowski/de Sitter background. We show that the same scheme works equally well for removing Ostrogradski’s ghost from fluctuations on a cosmological background in generic [Formula: see text]-type theories of gravity. As an application, we derive the general formula for the spectrum of primordial tensor perturbations from the stabilized theory. The evolution of matter density perturbations is also discussed.

Sensitivity and Robustness of Hydrodynamic Mooring Models

2002 ◽  
Vol 124 (4) ◽  
pp. 179-189 ◽  
Author(s):  
Joa˜o Paulo J. Matsuura ◽  
Michael M. Bernitsas ◽  
Luis O. Garza-Rios ◽  
Kazuo Nishimoto
Keyword(s):  
Design Methodology ◽  
Higher Order ◽  
Systematic Change ◽  
Mooring System ◽  
University Of Michigan ◽  
First Order ◽  
Global Properties ◽  
Higher Order Terms ◽  
The University ◽  
The Impact

Various hydrodynamic maneuvering models are available for modeling the slow motion horizontal plane dynamics of mooring and towing systems. In previous work, we compared four representative and widely used maneuvering models and assessed them based on the design methodology for mooring systems developed at the University of Michigan. In this paper, we study the impact of experimental uncertainties in the maneuvering coefficients on mooring system dynamic analysis. Uncertainties in higher order coefficients may even result in sign change as measured by different experimental facilities. This may indicate lack of robustness in maneuvering modeling. In our recent work, maneuvering models were classified in two schools of thought, each having a different set of coefficients subject to uncertainties. The first school is represented by the Abkowitz (A-M) and the Takashina (T-M) models, and the second by the Obokata (O-M) and the Short Wing (SW-M) models. The design methodology developed at the University of Michigan uses time independent global properties of mooring system dynamics to compare the maneuvering models, and assess their sensitivity and robustness. Equilibria, bifurcation sequences and associated morphogeneses, singularities of bifurcations, and secondary equilibrium paths are such global properties. Systematic change of important coefficients in each model shows that, for both schools of thought, sensitivity to first order terms is high while sensitivity to higher order terms is low. Accuracy in measurement of first order terms is high while accuracy in measurement of higher order terms is low. These two tendencies reduce each other’s impact, providing acceptable robustness.

scholarly journals Critical Combinations of Higher-Order Terms in Einstein-Maxwell Theory and Compactification

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Nahomi Kan ◽  
Kiyoshi Shiraishi
Keyword(s):  
Higher Order ◽  
De Sitter ◽  
Spontaneous Compactification ◽  
Maxwell Theory ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Inflationary Phase ◽  
Expansion Time ◽  
Higher Order Terms

We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, particularly in the background of spontaneous compactification. Two classes of theories are proposed in this paper. The first model as a generalization of the critical gravity with the Maxwell field could have a de Sitter solution. We consider the Lanczos-Lovelock term and Horndeski term as well as the higher-order Maxwell term for the second model, which contains a possible longer expansion time for the inflationary phase. It is interesting that both models can be regarded as the generalization of the Randjbar-Daemi, Salam and Strathdee (RSS) model and give the well behavior for inflation stage under the specific assumptions.

Hyperbolic Runge–Kutta Method Using Evolutionary Algorithm

2018 ◽  
Vol 13 (10) ◽  
Author(s):  
A. Arun Govind Neelan ◽  
Manoj T. Nair
Keyword(s):  
Evolutionary Algorithm ◽  
Stability Region ◽  
Strong Stability ◽  
Higher Order ◽  
Test Cases ◽  
Runge Kutta Method ◽  
Higher Order Terms ◽  
Runge Kutta ◽  
The Stability ◽  
Classical Optimization

A family of Runge–Kutta (RK) methods designed for better stability is proposed. Authors have optimized the stability of RK method by increasing the stability region by trading some of the higher order terms in the Taylor series. For flow involving shocks, compromising a few higher order terms will not affect convergence rate that is justified with an example. Though this kind of analysis began about three decades ago, most of the papers dealt with classical optimization and ended up in relatively nonoptimal values. Here, authors have overcome that by using evolutionary algorithm (EA), the result is refined using multisection method (MSM). The schemes designed based on this procedure have better stability than the classical RK methods, strong stability RK methods (SSPRK), and low dispersive and dissipative RK methods (LDDRK) of the same number of stages. Authors have tested the schemes on a variety of test cases and found some significant improvement.

scholarly journals Thin-shell wormholes in $$(2+1)$$-dimensional F(R) theories

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Cecilia Bejarano ◽  
Ernesto F. Eiroa ◽  
Griselda Figueroa-Aguirre
Keyword(s):  
Scalar Curvature ◽  
Thin Shell ◽  
Constant Scalar Curvature ◽  
De Sitter ◽  
Circular Symmetry ◽  
Theories Of Gravity ◽  
Thin Shell Wormholes ◽  
Stable Solutions ◽  
The Stability

AbstractWe construct a broad family of thin-shell wormholes with circular symmetry in $$(2+1)$$ ( 2 + 1 ) -dimensional F(R) theories of gravity, with constant scalar curvature R. We study the stability of the static configurations under perturbations preserving the symmetry. We present examples of charged thin-shell wormholes which are asymptotically anti-de Sitter at both sides of the throat. We show that stable solutions are possible when suitable values of the parameters are taken.

Estimates of Wave Elevations Around Structures

2010 ◽  
Author(s):  
Anne Katrine Bratland ◽  
Ragnvald Bo̸rresen ◽  
Per Ivar Barth Berntsen
Keyword(s):  
Water Depth ◽  
Wave Theory ◽  
Higher Order ◽  
Offshore Platforms ◽  
Test Results ◽  
Regular Wave ◽  
First Order ◽  
Wave Elevation ◽  
Higher Order Terms ◽  
Wave Elevations

When designing offshore platforms the still water air gap has to be large enough to avoid major wave-in-deck impact. Since wave elevation in harsh weather is highly non-linear, corrections to the calculated first order solution are necessary. The present method is a pragmatic approach to estimate the higher order contributions, utilizing the first order response amplitude operator and higher order wave elevations. For infinite water depth it is shown that regular wave theory is a good approximation for calculating second order wave elevation in irregular seas. So the higher order waves are calculated with regular wave theory, and the QTF and higher order terms are approximated by the first order RAO. Comparison with model test results have been performed for a GBS in moderate water depth and a semi-submersible is relatively deep water. The agreements with model tests are satisfactory.

scholarly journals Condensation of a scalar field non-minimally coupled to gravity in a cosmological context

2020 ◽  
Vol 35 (32) ◽  
pp. 2050270
Author(s):  
Amir Ghalee
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Condensed Phase ◽  
Condensed State ◽  
De Sitter ◽  
Cosmological Perturbations ◽  
Cosmological Context ◽  
Background Density ◽  
The Universe ◽  
Bonnet Term

We present a new mechanism to condense a scalar field coupled to the Gauss–Bonnet term. We propose a scenario in which the condensed state will emerge from the background energy density in the late-Universe. During the radiation and dust-dominated eras, the energy density of the scalar field, [Formula: see text], decreases at a slower rate than the background density. Eventually, [Formula: see text] dominates over the energy density of dust and the scalar field could be condensed. In the condensed phase, we have the de Sitter phase for the universe with [Formula: see text]. Moreover, we study the cosmological perturbations of the model and explore predictions of the model.

scholarly journals Cosmological Bounce and Some Other Solutions in Exponential Gravity

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 105 ◽  
Author(s):  
Pritha Bari ◽  
Kaushik Bhattacharya ◽  
Saikat Chakraborty
Keyword(s):  
Cosmological Constant ◽  
Cosmological Solution ◽  
Constant Term ◽  
Gravity Theory ◽  
De Sitter ◽  
Sitter Solution ◽  
Higher Derivative ◽  
New Type ◽  
Theories Of Gravity ◽  
Theory Of Gravity

In this work, we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric f ( R ) gravity where the form of the gravitational Lagrangian is given by 1 α e α R . In the low curvature limit this theory reduces to ordinary Einstein-Hilbert Lagrangian together with a cosmological constant term. Precisely because of this cosmological constant term this theory of gravity is able to support nonsingular bouncing solutions in both matter and vacuum background. Since for this theory of gravity f ′ and f ″ is always positive, this is free of both ghost instability and tachyonic instability. Moreover, because of the existence of the cosmological constant term, this gravity theory also admits a de-Sitter solution. Lastly we hint towards the possibility of a new type of cosmological solution that is possible only in higher derivative theories of gravity like this one.

Sign in / Sign up

Export Citation Format

Share Document