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

2018 ◽  
Vol 15 (12) ◽  
pp. 1850212 ◽  
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.

scholarly journals Dynamical system analysis for DBI dark energy interacting with dark matter

2015 ◽  
Vol 30 (02) ◽  
pp. 1550009 ◽  
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.

scholarly journals Revisiting dynamics of interacting quintessence

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Patrocinio Pérez ◽  
Ulises Nucamendi ◽  
Roberto De Arcia
Keyword(s):  
Dynamical System ◽  
Dark Matter ◽  
Phase Space ◽  
Scalar Field ◽  
Cosmic Time ◽  
Matter Density ◽  
Kinetic Term ◽  
Dynamical System Theory ◽  
Exponential Potential ◽  
Alpha Beta

AbstractWe apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field $$\phi $$ ϕ . For a coupling function $$Q = -(\alpha d\rho _m/dt + \beta d\rho _\phi /dt )$$ Q = - ( α d ρ m / d t + β d ρ ϕ / d t ) , where t is the cosmic time, we have found that it can be rewritten in the form $$Q = 3H (\alpha \rho _m + \beta (d\phi /dt)^2 )/(1-\alpha +\beta )$$ Q = 3 H ( α ρ m + β ( d ϕ / d t ) 2 ) / ( 1 - α + β ) , so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the scenarios $$\alpha =0$$ α = 0 , $$\alpha = \beta $$ α = β and $$\alpha = -\beta $$ α = - β , separately and in order to describe the cosmological evolution we have calculated various observables. A notable result of this work is that, unlike for the noninteracting scalar field with exponential potential where five critical points appear, in the case studied here, with the exception of the matter dominated solution, the remaining singular points are transformed into scaling solutions enriching the phase space. It is shown that for $$\alpha \ne 0$$ α ≠ 0 , a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature.

scholarly journals Dynamical System Perspective of Cosmological Models Minimally Coupled with Scalar Field

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
S. Surendra Singh ◽  
Chingtham Sonia
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
Fixed Points ◽  
Cosmic Acceleration ◽  
Stable Model ◽  
Exponential Potential ◽  
Total Energy Density ◽  
System Perspective ◽  
Special Cases ◽  
Potential Form

The stability criteria for the dynamical system of a homogeneous and isotropic cosmological model are investigated with the interaction of a scalar field in the presence of a perfect fluid. In this paper, we depict the dynamical system perspective to study qualitatively the scalar field cosmology under two special cases, with and without potential. In the absence of potential, we get a two-dimensional dynamical system, and we study the analytical as well as geometrical behavior. For the dynamical system with potential, we analyze different potential forms: simple exponential potential form (Vϕ=Voe−λϕ), double exponential potential form Vϕ=Voexp−Aexp2αϕ, and inverse power law potential form (Vϕ=Voϕ−α). We generate an autonomous system of ordinary differential equations (ASODE) for each case by introducing new dimensionless variables and obtain respective fixed points. We also analyze the type, nature, and stability of the fixed points and how their behavior reflects towards the cosmological scenarios. Throughout the whole work, the investigation of this model has shown us the deep connection between these theories and cosmic acceleration phenomena. The phase plots of the system at different conditions and different values of γ have been analyzed in detail, and their geometrical interpretations have been studied. The perturbation plots of the dynamical system have been analyzed with emphasis on our analytical findings. We have evaluated the total energy density (Ωϕ) at the fixed points and also found out the suitable range of γ and λ for a stable model.

scholarly journals Autonomous dynamical system approach for inflationary Gauss–Bonnet modified gravity

2018 ◽  
Vol 27 (05) ◽  
pp. 1850059 ◽  
Author(s):  
V. K. Oikonomou
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Phase Space ◽  
Modified Gravity ◽  
System Approach ◽  
De Sitter ◽  
Dynamical System Approach ◽  
Independent Variables ◽  
Perfect Fluids ◽  
Autonomous Dynamical System

In this paper, we shall analyze the [Formula: see text] gravity phase space, in the case that the corresponding dynamical system is autonomous. In order to make the dynamical system autonomous, we shall appropriately choose the independent variables, and we shall analyze the evolution of the variables numerically, emphasizing on the inflationary attractors. As we demonstrate, the dynamical system has only one de Sitter fixed point, which is unstable, with the instability being traced in one of the independent variables. This result holds true both in the presence and in the absence of matter and radiation perfect fluids. We argue that this instability could loosely be viewed as an indication of graceful exit in the [Formula: see text] theory of gravity.

scholarly journals Thermodynamics of de Sitter black holes with a conformally coupled scalar field

2005 ◽  
Vol 72 (2) ◽  
Author(s):  
Anne-Marie Barlow ◽  
Daniel Doherty ◽  
Elizabeth Winstanley
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
De Sitter

scholarly journals Open quantum entanglement: a study of two atomic system in static patch of de Sitter space

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Samim Akhtar ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Debopam Goswami ◽  
Sudhakar Panda ◽  
...  
Keyword(s):  
Scalar Field ◽  
Density Matrix ◽  
Master Equation ◽  
Quantum Entanglement ◽  
De Sitter Space ◽  
Thermal Bath ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Open Quantum ◽  
Non Locality

Abstract In this work, our prime objective is to study non-locality and long range effect of two body correlation using quantum entanglement from various information theoretic measure in the static patch of de Sitter space using a two body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result alongwith the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$$e'$$e′nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of De-Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.

Noncommutative scalar field in de Sitter space–time and pair creation process

2021 ◽  
Vol 36 (02) ◽  
pp. 2150011
Author(s):  
Nabil Mehdaoui ◽  
Lamine Khodja ◽  
Salah Haouat
Keyword(s):  
Scalar Field ◽  
Chemical Potential ◽  
De Sitter Space ◽  
Space Time ◽  
Pair Creation ◽  
De Sitter ◽  
Creation Process ◽  
Scalar Particles ◽  
Constant Electromagnetic Field

In this work, we address the process of pair creation of scalar particles in [Formula: see text] de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in [Formula: see text]. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies.

scholarly journals Dynamics of scalar potentials in theory of gravity

2019 ◽  
Vol 97 (8) ◽  
pp. 880-894
Author(s):  
M. Zubair ◽  
Farzana Kousar ◽  
Saira Waheed
Keyword(s):  
Scalar Field ◽  
Field Potential ◽  
Graphical Analysis ◽  
Chaplygin Gas ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Barotropic Fluid ◽  
First Case ◽  
De Sitter Universe

In this paper, we explore the nature of scalar field potential in [Formula: see text] gravity using a well-motivated reconstruction scheme for flat Friedmann–Robertson–Walker (FRW) geometry. The beauty of this scheme lies in the assumption that the Hubble parameter can be expressed in terms of scalar field and vice versa. Firstly, we develop field equations in this gravity and present some general explicit forms of scalar field potential via this technique. In the first case, we take the de Sitter universe model and construct some field potentials by taking different cases for the coupling function. In the second case, we derive some field potentials using the power law model in the presence of different matter sources like barotropic fluid, cosmological constant, and Chaplygin gas for some coupling functions. From graphical analysis, it is concluded that using some specific values of the involved parameters, the reconstructed scalar field potentials are cosmologically viable in both cases.

The dynamical system approach to scalar field cosmology

2000 ◽  
Vol 17 (8) ◽  
pp. 1783-1814 ◽  
Author(s):  
E Gunzig ◽  
V Faraoni ◽  
A Figueiredo ◽  
T M Rocha Filho ◽  
L Brenig
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
System Approach ◽  
Dynamical System Approach ◽  
Scalar Field Cosmology
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