Stiff matter solution in Brans–Dicke theory and the general relativity limit

Generally the Brans–Dicke (BD) theory reduces to general relativity (GR) in the limit [Formula: see text] if the scalar field goes as [Formula: see text]. However, it is also known that there are examples with [Formula: see text] that does not tend to GR. We discuss another case: a homogeneous and isotropic universe filled with stiff matter. The power of time dependence of these solutions does not depend on [Formula: see text], and there is no GR limit even though we have [Formula: see text]. A perturbative and a dynamical system analysis of this exotic case are carried out.

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Dynamical system analysis for DBI dark energy interacting with dark matter

Modern Physics Letters A ◽

10.1142/s0217732315500091 ◽

2015 ◽

Vol 30 (02) ◽

pp. 1550009 ◽

Cited By ~ 10

Author(s):

Nilanjana Mahata ◽

Subenoy Chakraborty

Keyword(s):

Dynamical System ◽

Dark Matter ◽

Dark Energy ◽

Scalar Field ◽

System Analysis ◽

Einstein Field Equation ◽

Field Equations ◽

Cosmological Scenario ◽

Kinetic Energy Term ◽

Autonomous Dynamical System

A dynamical system analysis related to Dirac–Born–Infeld (DBI) cosmological model has been investigated in this present work. For spatially flat FRW spacetime, the Einstein field equation for DBI scenario has been used to study the dynamics of DBI dark energy interacting with dark matter. The DBI dark energy model is considered as a scalar field with a nonstandard kinetic energy term. An interaction between the DBI dark energy and dark matter is considered through a phenomenological interaction between DBI scalar field and the dark matter fluid. The field equations are reduced to an autonomous dynamical system by a suitable redefinition of the basic variables. The potential of the DBI scalar field is assumed to be exponential. Finally, critical points are determined, their nature have been analyzed and corresponding cosmological scenario has been discussed.

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Dynamical system analysis for a scalar–tensor model with Gauss–Bonnet coupling

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500440 ◽

2019 ◽

Vol 16 (03) ◽

pp. 1950044

Author(s):

Behnaz Fazlpour ◽

Ali Banijamali

Keyword(s):

Dynamical System ◽

Dark Energy ◽

Scalar Field ◽

Critical Points ◽

System Analysis ◽

Field Potential ◽

Tensor Model ◽

Coincidence Problem ◽

Perturbation Matrix ◽

Dynamical System Method

In this paper, we study the dynamics of a scalar–tensor model of dark energy in which a scalar field that plays the role of dark energy, non-minimally coupled to the Gauss–Bonnet invariant in four dimensions. We utilize the dynamical system method to extract the critical points of the model and to conclude about their stability, we investigate the sign of the corresponding eigenvalues of the perturbation matrix at each point numerically. For exponential form of the scalar field potential and coupling function, we find five stable points among the critical points of the autonomous system. We also find four scaling attractor solutions with the property that the ratio of dark energy to dark matter density parameters are of order one. These solutions give the hope to alleviate the well-known coincidence problem in cosmology.

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Dynamical system analysis of Hessence scalar field in teleparallel gravity: Invariant manifold technique

International Journal of Modern Physics A ◽

10.1142/s0217751x19501562 ◽

2019 ◽

Vol 34 (28) ◽

pp. 1950156 ◽

Cited By ~ 1

Author(s):

Subhajyoti Pal ◽

Subenoy Chakraborty

Keyword(s):

Dynamical System ◽

Scalar Field ◽

Invariant Manifold ◽

Critical Points ◽

System Analysis ◽

Teleparallel Gravity ◽

Center Manifolds ◽

Field Equations ◽

Stability Diagrams ◽

Nonlinear Autonomous System

This paper investigates the cosmological dynamics of the Hessence scalar field coupled with the dark matter in the background of the teleparallel gravity. We have assumed that the potential of the scalar field is exponential in nature whereas the [Formula: see text] appearing in the teleparallel theory has the form [Formula: see text]. The field equations of this system reduce to a nonlinear autonomous system and dynamical system analysis is then performed. Due to the nonlinearity and the existence of multiple zero eigenvalues, the traditional procedures of analysis break down. So some novel technique is required. One of the latest such techniques is the invariant manifold theory. By the application of this theory, one projects the variables linked with the zero eigenvalues onto the variables linked with the nonzero eigenvalues to compute the center manifolds and the reduced systems associated with the critical points. These reduced systems reflect the nature of the whole dynamical systems. They also have less dimension and are often simple in nature. Hence, it is possible to solve them directly. In this paper, we work exactly in this spirit and find the center manifolds and solve the corresponding reduced system for some of the critical points associated with the dynamical system. We discover some interesting results namely that there are certain bounds on the interaction term [Formula: see text] which asserts the stability of the systems. We also present various stability diagrams of the reduced systems. An asymptotic analysis is then done for the critical points at infinity. Finally, we discuss the cosmological interpretation of our results.

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Dynamical system analysis of FLRW models with Modified Chaplygin gas

Scientific Reports ◽

10.1038/s41598-020-80396-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Ali Osman Yılmaz ◽

Ertan Güdekli

Keyword(s):

Dynamical System ◽

Equation Of State ◽

Energy Density ◽

System Analysis ◽

Chaplygin Gas ◽

Modified Chaplygin Gas ◽

State Spaces ◽

The Universe ◽

Matter Energy ◽

Far Future

AbstractWe investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume $$p=(\gamma -1)\mu -\dfrac{A}{\mu ^\alpha }$$ p = ( γ - 1 ) μ - A μ α as equation of state where $$\mu$$ μ is the matter-energy density, p is the pressure, $$\alpha$$ α is a parameter which can take on values $$0<\alpha \le 1$$ 0 < α ≤ 1 as well as A and $$\gamma$$ γ are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.

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WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194511001176 ◽

2011 ◽

Vol 03 ◽

pp. 87-97 ◽

Cited By ~ 5

Author(s):

F. P. POULIS ◽

J. M. SALIM

Keyword(s):

General Relativity ◽

Scalar Field ◽

Riemannian Geometry ◽

Axiomatic Approach ◽

Space Time ◽

Weyl Geometry ◽

Test Particles ◽

Variational Formalism ◽

Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

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Static spherically symmetric stiff matter in general relativity

Classical and Quantum Gravity ◽

10.1088/0264-9381/11/4/003 ◽

1994 ◽

Vol 11 (4) ◽

pp. L69-L72 ◽

Cited By ~ 8

Author(s):

Salah Haggag ◽

Joseph Hajj-Boutros

Keyword(s):

General Relativity ◽

Spherically Symmetric ◽

Stiff Matter

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Trunk control during standing reach: A dynamical system analysis of movement strategies in patients with mechanical low back pain

Gait & Posture ◽

10.1016/j.gaitpost.2008.10.053 ◽

2009 ◽

Vol 29 (3) ◽

pp. 370-376 ◽

Cited By ~ 56

Author(s):

Sheri P. Silfies ◽

Anand Bhattacharya ◽

Scott Biely ◽

Sue S. Smith ◽

Simon Giszter

Keyword(s):

Dynamical System ◽

Low Back Pain ◽

Back Pain ◽

System Analysis ◽

Low Back ◽

Trunk Control ◽

Movement Strategies

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Autonomous dynamical system description of de Sitter evolution in scalar assisted f(R) − ϕ gravity

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887818502122 ◽

2018 ◽

Vol 15 (12) ◽

pp. 1850212 ◽

Cited By ~ 10

Author(s):

K. Kleidis ◽

V. K. Oikonomou

Keyword(s):

Dynamical System ◽

Numerical Analysis ◽

Scalar Field ◽

Analysis Approach ◽

Single Variable ◽

De Sitter ◽

Exponential Potential ◽

System Description ◽

Variable Formula ◽

Autonomous Dynamical System

In this paper we will study the cosmological dynamical system of an [Formula: see text] gravity in the presence of a canonical scalar field [Formula: see text] with an exponential potential by constructing the dynamical system in a way that it is rendered autonomous. This feature is controlled by a single variable [Formula: see text], which when it is constant, the dynamical system is autonomous. We focus on the [Formula: see text] case which, as we demonstrate by using a numerical analysis approach, leads to an unstable de Sitter attractor, which occurs after [Formula: see text] [Formula: see text]-foldings. This instability can be viewed as a graceful exit from inflation, which is inherent to the dynamics of de Sitter attractors.

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Dynamical system analysis of three-form field dark energy model with baryonic matter

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8427-3 ◽

2020 ◽

Vol 80 (9) ◽

Author(s):

Soumya Chakraborty ◽

Sudip Mishra ◽

Subenoy Chakraborty

Keyword(s):

Dynamical System ◽

Dark Energy ◽

Cold Dark Matter ◽

System Analysis ◽

Evolution Equations ◽

Matter Field ◽

Baryonic Matter ◽

Form Field ◽

The Stability ◽

Manifold Theory

AbstractA cosmological model having matter field as (non) interacting dark energy (DE) and baryonic matter and minimally coupled to gravity is considered in the present work with flat FLRW space time. The DE is chosen in the form of a three-form field while radiation and dust (i.e; cold dark matter) are the baryonic part. The cosmic evolution is studied through dynamical system analysis of the autonomous system so formed from the evolution equations by suitable choice of the dimensionless variables. The stability of the non-hyperbolic critical points are examined by Center manifold theory and possible bifurcation scenarios have been examined.

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