Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models

Abstract

In this paper we investigate, from the dynamical systems perspective, the evolution of a Kantowski-Sachs metric in a generic class of $f(R)$ models. We present conditions (i. e., differentiability conditions, existence of minima, monotony intervals, etc.) for a free input function related to the $f(R)$, that guarantee the asymptotic stability of well-motivated physical solutions, specially, self-accelerated solutions, allowing to describe both inflationary- and late-time acceleration stages of the cosmic evolution. We discuss which $f(R)$ theories allows for a cosmic evolution with an acceptable matter era, in correspondence to the modern cosmological paradigm. We find a very rich behavior, and amongst others the universe can result in isotropized solutions with observables in agreement with observations, such as de Sitter, quintessence-like, or phantom solutions. Additionally, we find that a cosmological bounce and turnaround are realized in a part of the parameter-space as a consequence of the metric choice.

arXiv comment66 pages, 9 captioned figures, 10 tables. Matches the published version, with the exception of aesthetic details

References in corpus (103)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Planck 2013 results. XVI. Cosmological parameters
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Cosmological Constant and Dark Energy
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Extended Theories of Gravity
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• f(R,T) gravity
• The Case for a Positive Cosmological Lambda-term
• Cosmology and the Fate of Dilatation Symmetry
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Cur vature of the Universe Using Type Ia Supernovae
• Exponential potentials and cosmological scaling solutions
• Disappearing cosmological constant in f(R) gravity
• Dark Energy Constraints from the Cosmic Age and Supernova
• Quantum deSitter cosmology and phantom matter
• 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
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Quintom Cosmology: Theoretical implications and observations
• Cosmological Evolution of a Quintom Model of Dark Energy
• Conditions for the cosmological viability of f(R) dark energy models
• The Cosmology of Generalized Modified Gravity Models
• A classification of scalar field potentials with cosmological scaling solutions
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• Quantum effects can render w<-1 on cosmological scales
• The Power of General Relativity
• "Teleparallel" Dark Energy
• Relativistic cosmology and large-scale structure
• Curing singularities in cosmological evolution of F(R) gravity
• f(R,T) Cosmological Models in Phase Space
• Quintom models with an equation of state crossing -1
• Phase-Space analysis of Teleparallel Dark Energy
• Quintessence, super-quintessence and observable quantities in Brans-Dicke and non-minimally coupled theories
• Observational Constraints on Teleparallel Dark Energy
• Coupled oscillators as models of quintom dark energy
• General Relativistic 1+3 Orthonormal Frame Approach Revisited
• Quintom cosmologies admitting either tracking or phantom attractors
• Quintom cosmologies with arbitrary potentials
• Exact Solutions of Bianchi Types $I$ and $V$ Spacetimes in $f(R)$ Theory of Gravity
• On the evolution of universes in quadratic theories of gravity
• Dark energy from a quintessence (phantom) field rolling near potential minimum (maximum)
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• Bianchi type I cosmology with scalar and spinor fields
• Some remarks on the dynamical systems approach to fourth order gravity
• Shear dynamics in Bianchi I cosmologies with R^n-gravity
• Cosmological behavior in extended nonlinear massive gravity
• Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials
• Exact cosmological solutions of scale-invariant gravity theories
• Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity
• Dynamics of f(R)-cosmologies containing Einstein static models
• Bounce and cyclic cosmology in extended nonlinear massive gravity
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• Robust approach to f(R) gravity
• A new approach to reconstruction methods in $f(R)$ gravity
• Theoretical Limits on the Equation-of-State Parameter of Phantom Cosmology
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• Exponential-Potential Scalar Field Universes I: The Bianchi I Models
• On the Past Asymptotic Dynamics of Non-minimally Coupled Dark Energy
• Bounce behaviour in Kantowski-Sachs and Bianchi Cosmologies
• Generic feature of future crossing of phantom divide in viable $f(R)$ gravity models
• Quasi-dilaton non-linear massive gravity: Investigations of background cosmological dynamics
• Conditions for inflation in an initially inhomogeneous universe
• Noether and some other dynamical symmetries in Kantowski-Sachs model
• Oscillations of the F(R) dark energy in the accelerating universe
• Future Oscillations around Phantom Divide in f(R) Gravity
• The General Solution of Bianchi Type III Vacuum Cosmology
• Cosmological dynamics of fourth order gravity: A compact view
• On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity
• Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation
• f(R) Gravity and its Cosmological Implications
• $F(R)$ nonlinear massive theories of gravity and their cosmological implications
• Dynamical Systems in Cosmology
• Ricci Collineations of the Bianchi Types I and III, and Kantowski-Sachs Spacetimes
• Null Energy Condition Violation and Classical Stability in the Bianchi I Metric
• The dynamics of Bianchi I universes in $R^n$ cosmologies with torsion
• Updated constraints from the PLANCK experiment on modified gravity
• Stable super-inflating cosmological solutions in f(R)-gravity
• Bianchi IX model: Reducing phase space
• Phase-space of flat Friedmann-Robertson-Walker models with both a scalar field coupled to matter and radiation
• (Non) singular Kantowski-Sachs Universe from quantum spherically reduced matter
• Kantowski-Sachs universe cannot be closed
• Linear perturbations in viable f(R) theories
• About matter and dark-energy domination eras in R^n gravity or lack thereof
• Constraints on Modified Gravity from ACT and SPT
• Wormhole Solutions in the Kantowski--Sachs Spacetime
• Spherically symmetric cosmology: resource paper
• Global phase time and path integral for the Kantowski--Sachs anisotropic univers
• General behaviour of Bianchi VI_0 solutions with an exponential-potential scalar field
• Anisotropic higher derivative gravity and inflationary universe
• Asymptotic behaviour of Bianchi VI(o) solutions with an exponential potential scalar field

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• Kantowski-Sachs Einstein-æther perfect fluid models
• Instability of a Kerr black hole in f(R) gravity
• Correction to Lagrangian for Bouncing Cosmologies in $f(Q)$ Gravity
• Kantowski-Sachs Universes sourced by a Skyrme fluid
• Cosmological Evolution of Two-Scalar fields Cosmology in the Jordan frame
• Can $f(R)$ gravity isotropize a pre-bounce contracting universe?
• $f(\mathcal{G},\text{T})$ Gravity Bouncing Universe with Cosmological Parameters
• Interacting Quintessence in a New Scalar-Torsion Gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Kantowski-Sachs spherically symmetric solutions in teleparallel $F(T)$ gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• Hyperbolic inflation in the Jordan frame
• Kantowski-Sachs cosmology in scalar-torsion theory
• Cosmological evolutions of $F(R)$ nonlinear massive gravity
• Electromagnetic Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
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