Oscillatory behavior of closed isotropic models in second order gravity theory

Abstract

Homogeneous and isotropic models are studied in the Jordan frame of the second order gravity theory. The late time evolution of the models is analysed with the methods of the dynamical systems. The normal form of the dynamical system has periodic solutions for a large set of initial conditions. This implies that an initially expanding closed isotropic universe may exhibit oscillatory behaviour.

16 pages, 3 figures. With some minor improvements. To appear in General Relativity and Gravitation

References in corpus (27)

• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• The Pre-Big Bang Scenario in String Cosmology
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Gauss-Bonnet dark energy
• Conditions for the cosmological viability of f(R) dark energy models
• A Cyclic Model of the Universe
• The Cosmology of Generalized Modified Gravity Models
• Are f(R) dark energy models cosmologically viable ?
• Reconciling dark energy models with f(R) theories
• Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations
• On Physical Equivalence between Nonlinear Gravity Theories
• Limit to General Relativity in f(R) theories of gravity
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• The (pseudo)issue of the conformal frame revisited
• Inflation in Gauss-Bonnet Brane Cosmology
• On the evolution of universes in quadratic theories of gravity
• Oscillatory Universes in Loop Quantum Cosmology and Initial Conditions for Inflation
• Power-laws f(R) theories are cosmologically unacceptable
• Braneworld Cosmology in (Anti)--de Sitter Einstein--Gauss--Bonnet--Maxwell Gravity
• Bounce Conditions in f(R) Cosmologies
• The Ups and Downs of Cyclic Universes
• Metric gravity theories and cosmology. I. Physical interpretation and viability
• Compactifying the state space for alternative theories of gravity
• The recollapse problem of closed FRW models in higher-order gravity theories

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• Revisiting Fractional Cosmology
• Phase-space of flat Friedmann-Robertson-Walker models with both a scalar field coupled to matter and radiation
• The initial state of generalized radiation universes
• On stability of the Kasner solution in quadratic gravity
• Asymptotic solutions in f(R)-gravity
• Comment on "Existence of Einstein static universes and their stability in fourth-order theories of gravity"
• Cosmological Asymptotics in Higher-Order Gravity Theories