scholarly journals Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background

2016 ◽  
Vol 2016 ◽  
pp. 1-26 ◽  
Author(s):  
Bogdan Dănilă ◽  
Tiberiu Harko ◽  
Man Kwong Mak ◽  
Praiboon Pantaragphong ◽  
Sorin V. Sabau
Keyword(s):  
Stability Analysis ◽  
Scalar Field ◽  
Scalar Fields ◽  
Cosmological Evolution ◽  
Order System ◽  
Unstable State ◽  
Scalar Field Models ◽  
Klein Gordon ◽  
Cosmological Scalar ◽  
The Stability

We study the stability of the cosmological scalar field models by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In this approach, we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a “second geometrization” and considering them as paths of a semispray. By introducing a nonlinear connection and a Berwald-type connection associated with the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model. We obtain all the relevant geometric quantities, and we formulate the condition for Jacobi stability in scalar field cosmologies. We consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential. The Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases. We also investigate the stability of the phantom quintessence and tachyonic scalar field models, by lifting the first-order system to the tangent bundle. It turns out that in the presence of a power law potential both of these models are Jacobi unstable during the entire cosmological evolution.

INTERACTING GENERALIZED DARK ENERGY AND RECONSTRUCTION OF SCALAR FIELD MODELS

2013 ◽  
Vol 28 (38) ◽  
pp. 1350180 ◽  
Author(s):  
M. SHARIF ◽  
ABDUL JAWAD
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Dark Energy Model ◽  
Cold Dark Matter ◽  
Scalar Potential ◽  
Scalar Fields ◽  
Phantom Divide ◽  
Evolution Parameter ◽  
Scalar Field Models ◽  
Phantom Divide Line

In this paper, we consider the interacting generalized dark energy with cold dark matter and analyze the behavior of evolution parameter via dark energy and interacting parameters. It is found that the evolution parameter crosses the phantom divide line in most of the cases of integration constants. We also establish the correspondence of scalar field models (quintessence, k-essence and dilaton) with this dark energy model in which scalar fields show the increasing behavior. The scalar potential corresponds to attractor solutions in quintessence case.

Real scalar field solutions of the EKG equations including matter

2020 ◽  
pp. 2150009
Author(s):  
A. Cabo Montes de Oca ◽  
D. Suarez Fontanella
Keyword(s):  
Dark Matter ◽  
Gravitational Field ◽  
Scalar Field ◽  
Scalar Fields ◽  
Stationary Solutions ◽  
Field Interaction ◽  
Small Bodies ◽  
Real Scalar ◽  
Static Solutions ◽  
Klein Gordon

Static (not stationary) solutions of the Einstein–Klein–Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of static solutions in contraposition with the case of the simpler EKG equations for real scalar fields and gravity. Surprisingly, when the considered matter is a photon-like gas, it turns out that the gravitational field intensity at large radial distances becomes nearly a constant, exerting an approximately fixed force to small bodies at any distance. The effect is clearly related with the massless character of the photon-like field. It is also argued that the gravitational field can generate a bounding attraction, that could avoid the unlimited increase in mass with the radius of the obtained here solution. This phenomenon, if verified, may furnish a possible mechanism for explaining how the increasing gravitational potential associated to dark matter, finally decays at large distances from the galaxies. A method for evaluating these photon bounding effects is just formulated in order to be further investigated.

Crowd Evacuation Stability Based on Self-Organized Criticality Theory

2014 ◽  
Vol 501-504 ◽  
pp. 2403-2406 ◽  
Author(s):  
Rong Yong Zhao ◽  
Jian Wang ◽  
Wei Qing Ling
Keyword(s):  
Stability Analysis ◽  
Complex Problem ◽  
Unstable State ◽  
Sand Pile ◽  
Mapping Model ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Crowd Evacuation ◽  
Crowd Motion ◽  
The Stability

In emergency, the crowd evacuation from public buildings is the most important issue to save human lives. Panic generation and spread normally can lead to the unstable state -stampede during the crowd motion. The stability of crowd evacuation is a complex problem being researched for decades. This paper introduces self-organized criticality(SOC) theory to build the mapping model from a collective crowd into a sand pile with SOC. Therefore, the complex problem of stability analysis for crowd evacuation is converted into sandpiper stability analysis in a relatively simpler way.

scholarly journals THE QUANTUM THEORY OF SCALAR FIELDS ON THE DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2563-2577 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN ◽  
ADRIAN POP
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Scalar Fields ◽  
Wave Functions ◽  
De Sitter ◽  
Scalar Quantum ◽  
Long Time ◽  
Klein Gordon ◽  
Free Scalar ◽  
Special Time

New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein–Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well known for long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.

scholarly journals Correspondence off(R,∇R)Modified Gravity with Scalar Field Models

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Abdul Jawad ◽  
Ujjal Debnath
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
State Parameter ◽  
Scalar Fields ◽  
Frw Universe ◽  
Tachyonic Field ◽  
Energy Models ◽  
The Stability ◽  
Scalar Potentials ◽  
The Universe

This paper is devoted to study the scalar field dark energy models by taking its different aspects in the framework off(R,∇R)gravity. We consider flat FRW universe to construct the equation of state parameter governed byf(R,∇R)gravity. The stability of the model is discussed with the help of squared speed of sound parameter. It is found that models show quintessence behavior of the universe in stable as well as unstable modes. We also develop the correspondence off(R,∇R)model with some scalar field dark energy models like quintessence, tachyonic field,k-essence, dilaton, hessence, and DBI-essence. The nature of scalar fields and corresponding scalar potentials is being analyzed inf(R,∇R)gravity graphically which show consistency with the present day observations about accelerated phenomenon.

Scalar fields in f(G) gravity

2020 ◽  
Vol 17 (09) ◽  
pp. 2050132
Author(s):  
Dog̃ukan Taṣer ◽  
Melis Ulu Dog̃ru
Keyword(s):  
Scalar Field ◽  
Bianchi Type ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Type I ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Massive Scalar Field ◽  
Scalar Field Models ◽  
Bianchi Type I Universe

In this study, we investigated scalar field in [Formula: see text]-gravity by using LRS Bianchi type-I universe. Massless and massive scalar field models are separately constructed in [Formula: see text]-gravity. Massless scalar field models are examined in the cases of constant and exponential potential fields. For all models, solutions of field equations are obtained under the consideration of [Formula: see text]. [Formula: see text] functions for each model are separately attained in theory. It is shown that constructed models in the presence of massless scalar field permit quintessence scalar field. Also, it is observed that each model indicates expanding universe with deceleration. Also, kinematical quantities are analyzed in the light of obtained solutions. All models are concluded with a geometric and physical perspective.

scholarly journals PHANTOM UNIVERSE FROM CPT SYMMETRIC QFT

2006 ◽  
Vol 15 (08) ◽  
pp. 1299-1310 ◽  
Author(s):  
ALEXANDER A. ANDRIANOV ◽  
FRANCESCO CANNATA ◽  
ALEXANDER Y. KAMENSHCHIK
Keyword(s):  
Field Theory ◽  
Dark Energy ◽  
Scalar Field ◽  
Complex Potential ◽  
Vacuum Energy ◽  
Scalar Fields ◽  
Smooth Transition ◽  
Cpt Symmetry ◽  
Energy Equivalence ◽  
Cosmological Scalar

We develop a generalization of semiclassical field theory for the case of non-Hermitian Hamiltonians with CPT symmetry and construct a classical cosmological, scalar-field based model describing a smooth transition from ordinary dark energy to the phantom one. Our model arises from a Lagrangian with a complex potential leading to a non-trivial vacuum with real vacuum energy. Equivalence with models involving two scalar fields one of which is phantom-like is discussed.

A study of the bulk viscous pressure in scalar fields and holographic Ricci dark energy considered in the modified gravity framework

2020 ◽  
Vol 98 (7) ◽  
pp. 664-674 ◽  
Author(s):  
Sthiti Chakrabarti ◽  
Surajit Chattopadhyay ◽  
Irina Radinschi
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Bulk Viscosity ◽  
Modified Gravity ◽  
Scalar Fields ◽  
Effective Equation ◽  
Ricci Dark Energy ◽  
Scalar Field Models ◽  
Viscous Pressure ◽  
Bulk Viscous Pressure

The work presented in this paper reports a rigorous study of the reconstruction of the modified gravity in the framework of the scalar field models of dark energy and holographic Ricci dark energy, a generalized version of the holographic dark energy presented in S. Nojiri and S.D. Odintsov. Gen. Relativ. Gravitation, 38, 1285 (2006). The tachyon and quintessence scalar fields have been considered and the cosmology associated with the presence of bulk viscosity has been studied. In the first part of our study, we have demonstrated the behaviour of the bulk viscosity coefficient in the framework of the reconstructed tachyon scalar field model of dark energy. The scale factor is chosen in the form a(t) = a0tβ, where β > 0. Two scalar field models, namely, tachyon and quintessence, have been considered in the framework of the modified field equations through incorporation of the bulk viscous pressure. The reconstructed density and pressure of the scalar field models have been explored for the cosmological consequences in the presence of bulk viscosity. The behaviour of the effective equation of state parameters has been investigated. Finally, we have reconstructed f(T) gravity in the presence of holographic Ricci dark energy and a transition of the effective equation of state parameter from quintessence to phantom has been observed.

scholarly journals ABOUT BLACK HOLES WITH NONTRAPPING INTERIOR

1999 ◽  
Vol 14 (13) ◽  
pp. 2013-2022 ◽  
Author(s):  
ALEJANDRO CABO ◽  
ELOY AYÓN
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Generalized Functions ◽  
Interior Solution ◽  
Schwarzschild Solution ◽  
Exterior Region ◽  
Trapped Surfaces ◽  
Proper Mass ◽  
Klein Gordon ◽  
Black Hole Solutions

Physical arguments related with the existence of black hole solutions having a non-trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field approaching a constant value at the horizon are given. It is argued that the coupled Einstein–Klein–Gordon equations can be satisfied in the sense of the generalized functions after removing a particular regularization designed for matching the interior solution with an external Schwarzschild space–time. The scalar field appears as just avoiding the appearance of closed trapped surfaces while coming from the exterior region. It also follows that the usual space integral over [Formula: see text] in the internal region just gives the total proper mass associated to the external Schwarzschild solution, as it should be expected.

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