Averaging reductions and asymptotic theorems are derived for oscillatory scalar fields, with exact quadrature solutions for t(a), phi(a), and H(a) in general relativistic, anisotropic, and brane-world cosmologies.
Dynamical systems in cosmology
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abstract
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. We begin with a brief review of dynamical systems theory. We then discuss cosmological models as dynamical systems and point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss some results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss some isotropic cosmological models derived from the string effective action.
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Power-law and logarithmic coupling models in covariant f(Q) gravity reproduce radiation, matter, and dark energy eras through dynamical systems analysis of critical points and their stability.
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Asymptotic Theorems and Averaging in Scalar Field Cosmology
Averaging reductions and asymptotic theorems are derived for oscillatory scalar fields, with exact quadrature solutions for t(a), phi(a), and H(a) in general relativistic, anisotropic, and brane-world cosmologies.
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An Interplay Between Fractional Calculus and Holographic Dark Energy
Introduces Fractional Holographic Dark Energy (FHDE) via fractionally corrected entropy from a modified Wheeler-DeWitt equation and studies its late-time cosmology, field reconstructions, and extensions to modified gravity theories.
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Dynamical analysis of the covariant $f(Q)$ gravity models
Power-law and logarithmic coupling models in covariant f(Q) gravity reproduce radiation, matter, and dark energy eras through dynamical systems analysis of critical points and their stability.