Dynamical systems of cosmological models for different possibilities of $G$ and ${\rho }_{\Lambda }$

Abstract

The present paper deals with the dynamics of spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model with a time varying cosmological constant $\Lambda$ where $\Lambda$ evolves with the cosmic time (t) through the Hubble parameter (H). We consider that the model dynamics has a reflection symmetry $H\to -H$ with $\Lambda (H)$ expressed in the form of Taylor series with respect to H. Dynamical systems for three different cases based on the possibilities of gravitational constant G and the vacuum energy density ${\rho }_{\Lambda }$ have been analysed. In Case I, both G and ${\rho }_{\Lambda }$ are taken to be constant. We analyse stability of the system by using the notion of spectral radius, behavior of perturbation along each of the axis with respect to cosmic time and Poincare sphere. In Case II, we have dynamical system analysis for G=constant and ${\rho }_{\Lambda }\ne$ constant where we study stability by using the concept of spectral radius and perturbation function. In Case III, we take $G\ne$ constant and ${\rho }_{\Lambda }\ne$ constant where we introduce a new set of variables to set up the corresponding dynamical system. We find out the fixed points of the system and analyse the stability from different directions: by analysing behaviour of the perturbation along each of the axis, Center Manifold Theory and stability at infinity using Poincare sphere respectively. Phase plots and perturbation plots have been presented. We deeply study the cosmological scenario with respect to the fixed points obtained and analyse the late time behavior of the Universe. Our model agrees with the fact that the Universe is in the epoch of accelerated expansion. The EOS parameter ${\omega }_{eff}$, total energy density ${\Omega }_{tt}$ are also evaluated at the fixed points for each of the three cases and these values are in agreement with the observational values in [1].

arXiv comment43 pages, 20 figures

References in corpus (56)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Cosmological Constant and Dark Energy
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Cosmological parameters from SDSS and WMAP
• The Second Data Release of the Sloan Digital Sky Survey
• Extra force in $f(R)$ modified theories of gravity
• Inhomogeneous Equation of State of the Universe: Phantom Era, Future Singularity and Crossing the Phantom Barrier
• BVRI Light Curves for 22 Type Ia Supernovae
• The Third Data Release of the Sloan Digital Sky Survey
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Dark Energy Dominance and Cosmic Acceleration in First Order Formalism
• Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature
• Covariant conservation of energy momentum in modified gravities
• Cosmological constant and vacuum energy: old and new ideas
• Generalized curvature-matter couplings in modified gravity
• An Improved Distance to NGC 4258 and its Implications for the Hubble Constant
• On the possible running of the cosmological "constant"
• The scaling evolution of cosmological constant
• Local determination of the Hubble constant and the deceleration parameter
• Dark energy as the weight of violating energy conservation
• Effective Action of Vacuum: Semiclassical Approach
• Variable Cosmological Constant as a Planck Scale Effect
• Running G and Λat low energies from physics at M_X: possible cosmological and astrophysical implications
• The $H_0$ tension in light of vacuum dynamics in the Universe
• Dark energy: a quantum fossil from the inflationary Universe?
• A Generalization to the Rastall Theory and Cosmic Eras
• Expansion History with Decaying Vacuum: A Complete Cosmological Scenario
• Testing the running of the cosmological constant with Type Ia Supernovae at high z
• Running vacuum against the $H_0$ and ${\sigma }_8$ tensions
• Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem
• The Cosmological Constant Problem and Running Vacuum in the Expanding Universe
• Density perturbations for running vacuum: a successful approach to structure formation and to the ${\sigma }_8$-tension
• Cosmologies with a time dependent vacuum
• Running vacuum in quantum field theory in curved spacetime: renormalizing ${\rho }_{vac}$ without $\sim m^4$ terms
• Gravitational and Chiral Anomalies in the Running Vacuum Universe and Matter-Antimatter Asymmetry
• Can dark energy be expressed as a power series of the Hubble parameter?
• Cosmological consequences in the framework of generalized Rastall theory of gravity
• Matter Non-conservation in the Universe and Dynamical Dark Energy
• CosMIn: The Solution to the Cosmological Constant Problem
• Stringy-Running-Vacuum-Model Inflation: from primordial Gravitational Waves and stiff Axion Matter to Dynamical Dark Energy
• $\Lambda (t)$ cosmology induced by a slowly varying Elko field
• Consequences of energy conservation violation: Late time solutions of $\Lambda (T)CDM$ subclass of $f(R,T)$ gravity using dynamical system approach
• Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
• Cosmological implications and structure formation from a time varying vacuum
• Cosmic evolution of dark energy in a generalized Rastall gravity
• Decay Law of Relativistic Particles: Quantum Theory Meets Special Relativity
• Fundamental constants and cosmic vacuum: the micro and macro connection
• Dynamical system approach to running $\Lambda$ cosmological models
• Supersymmetry, Cosmological Constant and Inflation: Towards a fundamental cosmic picture via "running vacuum"
• Generalising the coupling between spacetime and matter
• Non-minimal coupling inspires the Dirac cosmological model

Cited by in corpus (2)

• Qualitative Stability Analysis of Cosmological Parameters in $f(T,B)$ Gravity
• Scale-dependent gravity and covariant scale-setting