Perturbations of the Lambda-CDM model in a dynamical systems perspective

Abstract

The observational success and simplicity of the $\Lambda$CDM model, and the explicit analytic perturbations thereof, set the standard for any alternative cosmology. It therefore serves as a comparison ground and as a test case for methods which can be extended and applied to other cosmological models. In this paper we introduce dynamical systems and methods to describe linear scalar and tensor perturbations of the $\Lambda$CDM model, which serve as pedagogical examples that show the global illustrative powers of dynamical systems in the context of cosmological perturbations. We also study the asymptotic properties of the shear and Weyl tensors and discuss the validity of the perturbations as approximations to the Einstein field equations. Furthermore, we give a new approximation for the linear growth rate, $f(z)=\frac{d\ln \delta }{d\ln a}={\Omega }_m^{\frac{6}{11}}-\frac{1}{70}(1-{\Omega }_m{)}^{\frac{5}{2}}$, where $z$ is the cosmological redshift, ${\Omega }_m={\Omega }_m(z)$, while $a$ is the background scale factor, and show that it is much more accurate than the previous ones in the literature.

31 pages, 7 figures; v3. matches final published version

References in corpus (15)

• Cluster Abundance Constraints on Quintessence Models
• Cosmological perturbations
• Formulae for Growth Factors In Expanding Universes Containing Matter and a Cosmological Constant
• Asymptotic isotropization in inhomogeneous cosmology
• Global dynamics and inflationary center manifold and slow-roll approximants
• Dynamical system analysis at background and perturbation levels: Quintessence in severe disadvantage comparing to $\Lambda$CDM
• Testing for dynamical dark energy models with redshift-space distortions
• Recent developments concerning generic spacelike singularities
• Cosmological Perturbation Theory Revisited
• Second order cosmological perturbations: simplified gauge change formulas
• Dynamics of cosmological perturbations at first and second order
• fNL - gNL mixing in the matter density field at higher orders
• Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
• Dust-Radiation Universes: Stability Analysis
• A simplified structure for the second order cosmological perturbation equations

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• Background evolution and growth of structures in interacting dark energy through dynamical system analysis
• Exact solutions and cosmological constraints in fractional cosmology
• Cosmological perturbations and dynamical analysis for interacting quintessence
• Stability analysis of f(Q) gravity models using dynamical systems
• Time-averaging axion-like interacting scalar fields models
• Asymptotic behavior of $N$-fields Chiral Cosmology
• Dynamical systems in perturbative scalar field cosmology
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models
• Inflationary equilibrium configurations of scalar-tensor theories of gravity