Stable Exact Solutions in Cosmological Models with Two Scalar Fields

Abstract

The stability of isotropic cosmological solutions for two-field models in the Bianchi I metric is considered. We prove that the sufficient conditions for the Lyapunov stability in the Friedmann-Robertson-Walker metric provide the stability with respect to anisotropic perturbations in the Bianchi I metric and with respect to the cold dark matter energy density fluctuations. Sufficient conditions for the Lyapunov stability of the isotropic fixed points of the system of the Einstein equations have been found. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for string field theory inspired cosmological models.

arXiv comment23 pages, v3:typos corrected, references added

References in corpus (29)

• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Modeling the fifth dimension with scalars and gravity
• Quintom Cosmology: Theoretical implications and observations
• Cosmic Evolution in a Cyclic Universe
• Cosmological Evolution of a Quintom Model of Dark Energy
• Effective Field Theory for Inflation
• Is there Supernova Evidence for Dark Energy Metamorphosis ?
• Crossing the Phantom Divide: Theoretical Implications and Observational Status
• Crossing of the w=-1 Barrier by D3-brane Dark Energy Model
• Cosmological Limits on Slightly Skew Stresses
• Theory of cosmological perturbations in an anisotropic universe
• Oriented Open-Closed String Theory Revisited
• Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
• Quintom cosmologies admitting either tracking or phantom attractors
• Quintom cosmologies with arbitrary potentials
• Exactly Solvable SFT Inspired Phantom Model
• P-nflation: generating cosmic Inflation with p-forms
• Attractor Behavior of Phantom Cosmology
• Time Lumps in Nonlocal Stringy Models and Cosmological Applications
• Tachyon condensation in cubic superstring field theory
• On the Null Energy Condition and Cosmology
• Stringy Dark Energy Model with Cold Dark Matter
• Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
• Construction of Exact Solutions in Two-Fields Models and the Crossing of the Cosmological Constant Barrier
• Toward Open-Closed String Theoretical Description of Rolling Tachyon
• Noncommutative Field Theories and (Super)String Field Theories
• Null Energy Condition Violation and Classical Stability in the Bianchi I Metric
• String Inspired Quintom Model with Non-minimally Coupled Modified Gravity
• Cosmological models from a dynamical systems perspective

Cited by in corpus (32)

• Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials
• Two scalar field cosmology: Conservation laws and exact solutions
• De Sitter Universe in Nonlocal Gravity
• Integrable cosmological models with non-minimally coupled scalar fields
• Exact Solutions in Chiral Cosmology
• Reconstruction Procedure in Nonlocal Cosmological Models
• Reconstruction of Scalar Potentials in Modified Gravity Models
• Cosmological Solutions of a Nonlocal Model with a Perfect Fluid
• Some remarks about non-minimally coupled scalar field models
• Analysis of scalar perturbations in cosmological models with a non-local scalar field
• Revisiting Fractional Cosmology
• Extended phase-space analysis of the Horava-Lifshitz cosmology
• Cosmological Solutions in Multiscalar Field Theory
• Superpotential method for chiral cosmological models connected with modified gravity
• Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields
• Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory
• An anisotropic bouncing universe in non-local gravity
• Integrable modified gravity cosmological models with an additional scalar field
• Superpotential method for $F(R)$ cosmological models
• Anisotropic power-law inflation for a model of two scalar and two vector fields
• Inflation as an attractor in scalar cosmology
• Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Anisotropic hyperbolic inflation for a model of two scalar and two vector fields
• General solutions to $\mathcal{N}$-field cosmology with exponential potentials
• Dynamics of Potentials in Bianchi Type Scalar-Tensor Cosmology
• Quintessence scalar field and cosmological constant: Dynamics of a multi-component dark energy model
• Compact and extended objects from self-interacting phantom fields
• New exact solutions in multi-scalar field cosmology
• Anisotropic solutions for $R^2$ gravity model with a scalar field
• New Integrable Chiral Cosmological Models with Two Scalar Fields
• Integrable Cosmological Models with an Arbitrary Number of Scalar Fields