Dynamic properties of cyclic cosmologies

Abstract

Our first goal in this work is to study general and model-independent properties of cyclic cosmologies. The large number of studies of bouncing cosmologies and different cyclic scenarios published recently calls for a proper understanding of the universal properties of cyclic models. We thus first review and further elaborate the common physical and geometrical properties of various classes of cyclic models and then discuss how cyclic Universe can be treated as a dynamic system. We then discuss how two theorems from dynamic systems analysis can be used to ensure the existence of cyclic cosmological solutions under certain conditions on the field equations. After this we proceed towards our second goal which is the application of the obtained results to different frameworks of modified gravity theories: $f(R)$ gravity, dynamic dark energy and $f(T)$ gravity. We discuss the general requirements for the existence of cyclic solutions in these theories and also obtain various examples of cyclic cosmologies, while discussing their basic properties.

45 pages, 6 figures

References in corpus (27)

• Dynamics of dark energy
• Big-Bang Nucleosynthesis
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Stability of Cosmological Solution in f(R) Models of Gravity
• Degrees of freedom of $f(T)$ gravity
• Dark Matter from R^2-gravity
• Non-Singular Bouncing Universes in Loop Quantum Cosmology
• Energy-Momentum Squared Gravity
• Fourth order gravity: equations, history, and applications to cosmology
• A new kind of cyclic universe
• Lectures on the Cosmological Constant Problem
• The $\bar{\Lambda }CDM$ cosmology: from inflation to dark energy through running $\Lambda$
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Constraining f(R) gravity in solar system, cosmology and binary pulsar systems
• Interacting Dark Energy in f(T) cosmology : A Dynamical System analysis
• New observational constraints on $f(T)$ cosmology from radio quasars
• On dynamical systems approaches and methods in $f(R)$ cosmology
• Holographic bounce
• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
• Cyclic cosmology from Lagrange-multiplier modified gravity
• Kerr geometry in f(T) gravity
• Vector Perturbations in a Contracting Universe
• $\Lambda$CDM Bounce Cosmology without $\Lambda$CDM: the case of modified gravity
• Exact solutions, finite time singularities and non-singular universe models from a variety of $\Lambda (t)$ cosmologies
• A Cyclic Universe With Varying Cosmological Constant in $f(R,T)$ gravity
• Dynamical Analysis of an $n-H-T$ Cosmological Quintessence Real Gas Model with a General Equation of State
• Bouncing Cosmologies

Cited by in corpus (6)

• Creation of wormholes during the cosmological bounce
• A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature
• A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity
• Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology
• Geodesically complete cyclic cosmologies and entropy
• Cosmological bounce and the cosmological constant problem