Cosmological models and centre manifold theory

Abstract

Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type III with collisionless matter. In addition some statements in the literature on solutions of the Einstein equations coupled to a massive scalar field are proved rigorously.

17 pages

References in corpus (1)

• On the Einstein-Vlasov system with hyperbolic symmetry

Cited by in corpus (31)

• The Einstein-Vlasov System/Kinetic Theory
• Asymptotic behaviour of the Einstein-Vlasov system with a positive cosmological constant
• The Einstein-Vlasov system/Kinetic theory
• Theorems on existence and global dynamics for the Einstein equations
• Qualitative dynamics and inflationary attractors in loop cosmology
• Dynamics of dark energy models and centre manifolds
• Interacting 3-form dark energy models: distinguishing interactions and avoiding the Little Sibling of the Big Rip
• Global dynamics and inflationary center manifold and slow-roll approximants
• Dynamical systems in cosmology
• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• Late-time oscillatory behaviour for self-gravitating scalar fields
• Cosmic infinity: A dynamical system approach
• The Einstein-Vlasov sytem/Kinetic theory
• The recollapse problem of closed FRW models in higher-order gravity theories
• Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Dynamical system approach of non-minimal coupling in AdS/CFT cosmology
• On the oscillations and future asymptotics of locally rotationally symmetric Bianchi type III cosmologies with a massive scalar field
• The dynamical behaviour of homogeneous scalar-field spacetimes with general self-interaction potentials
• Genericity of blackhole formation in the gravitational collapse of homogeneous self-interacting scalar fields
• Isotropization of Slowly Expanding Spacetimes
• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Interacting Models of Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
• Covariant and gauge-invariant linear scalar perturbations in multiple scalar field cosmologies
• Quintessential and phantom power-law solutions in scalar tensor model of dark energy
• Generalized Model of Interacting Dark Energy and Dark Matter : Phase Portrait Analysis of Evolving Universe
• Kantowski-Sachs cosmology with Vlasov matter
• Global portraits of nonminimal inflation
• Particle Production Scenario in an Algebraically Coupled Quintessence Field with a Dark Matter Fluid
• The Einstein-Vlasov system
• Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry