New dynamical systems variables for coupled axion-saxion fields yield a general non-geodesicity expression at fixed points and identify genuinely non-geodesic attractors under exponential couplings.
Dynamical systems applied to cosmology: dark energy and modified gravity
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.
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Quintessence potential decreases monotonically with redshift while kinetic energy crosses zero near z=1, with negative values at intermediate redshifts being statistical artifacts from derivative reconstruction.
Exponential quintessence with an assumed kination epoch relaxes the dark energy fine-tuning problem by dozens of orders of magnitude relative to a cosmological constant.
Dynamical systems analysis of a Palatini k-essence model identifies fixed points for quasi-de-Sitter epochs, scaling solutions, and quintessence phases connected by heteroclinic orbits in flat FLRW cosmology.
A non-canonical generalized Brans-Dicke theory admits background cosmological solutions matching Lambda CDM characteristics for constant, power-law, and exponential potentials, with dynamics distinct from other scalar-tensor models.
For an exponential quintessence potential, an analytic formula links the current equation-of-state w_φ0 to the potential slope λ while enforcing prior radiation and matter domination, yielding the bound λ < 1.94 at Ω_φ0 = 0.685.
HDE models with future event horizon IR cutoff partially ease the Hubble tension while Hubble-scale cutoffs do not, consistent across six models and multiple BAO/SN/CMB combinations.
Interacting k-essence dark energy and non-pressureless dark matter models with two interaction forms are shown to reproduce major cosmological epochs and fit observations comparably to LambdaCDM while admitting late-time de Sitter attractors.
citing papers explorer
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Extending the Dynamical Systems Toolkit: Coupled Fields in Multiscalar Dark Energy
New dynamical systems variables for coupled axion-saxion fields yield a general non-geodesicity expression at fixed points and identify genuinely non-geodesic attractors under exponential couplings.
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Model-Independent Reconstruction of Quintessence Potential and Kinetic Energy from DESI DR2 and Pantheon+ Supernovae
Quintessence potential decreases monotonically with redshift while kinetic energy crosses zero near z=1, with negative values at intermediate redshifts being statistical artifacts from derivative reconstruction.
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Exponential Quintessence Model: Analytical Quantification of the Fine-Tuning Problem in Dark Energy
Exponential quintessence with an assumed kination epoch relaxes the dark energy fine-tuning problem by dozens of orders of magnitude relative to a cosmological constant.
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Dynamical system analysis of the cosmological phases in Palatini $k$-essence gravity
Dynamical systems analysis of a Palatini k-essence model identifies fixed points for quasi-de-Sitter epochs, scaling solutions, and quintessence phases connected by heteroclinic orbits in flat FLRW cosmology.
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Cosmological Dynamics of a Non-Canonical Generalised Brans-Dicke Theory
A non-canonical generalized Brans-Dicke theory admits background cosmological solutions matching Lambda CDM characteristics for constant, power-law, and exponential potentials, with dynamics distinct from other scalar-tensor models.
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Exponential Quintessence: Analytic Relationship Between the Current Equation of State Parameter and the Potential Parameter
For an exponential quintessence potential, an analytic formula links the current equation-of-state w_φ0 to the potential slope λ while enforcing prior radiation and matter domination, yielding the bound λ < 1.94 at Ω_φ0 = 0.685.
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Revisiting the Hubble tension problem in the framework of holographic dark energy
HDE models with future event horizon IR cutoff partially ease the Hubble tension while Hubble-scale cutoffs do not, consistent across six models and multiple BAO/SN/CMB combinations.
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Interacting $k$-essence field with non-pressureless Dark Matter: Cosmological Dynamics and Observational Constraints
Interacting k-essence dark energy and non-pressureless dark matter models with two interaction forms are shown to reproduce major cosmological epochs and fit observations comparably to LambdaCDM while admitting late-time de Sitter attractors.