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.

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

References in corpus (39)

• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Cosmology and the Fate of Dilatation Symmetry
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• 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
• Cosmological Evolution of a Quintom Model of Dark Energy
• Conditions for the cosmological viability of f(R) dark energy models
• Relativistic cosmology and large-scale structure
• f(R,T) Cosmological Models in Phase Space
• Coupled oscillators as models of quintom dark energy
• Quintom cosmologies admitting either tracking or phantom attractors
• Quintom cosmologies with arbitrary potentials
• On the evolution of universes in quadratic theories of gravity
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• Some remarks on the dynamical systems approach to fourth order gravity
• Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials
• 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
• 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
• Future Oscillations around Phantom Divide in f(R) Gravity
• The General Solution of Bianchi Type III Vacuum Cosmology
• f(R) Gravity and its Cosmological Implications
• $F(R)$ nonlinear massive theories of gravity and their cosmological implications
• Null Energy Condition Violation and Classical Stability in the Bianchi I Metric
• Updated constraints from the PLANCK experiment on modified gravity
• Phase-space of flat Friedmann-Robertson-Walker models with both a scalar field coupled to matter and radiation
• Linear perturbations in viable f(R) theories
• Spherically symmetric cosmology: resource paper
• Anisotropic higher derivative gravity and inflationary universe
• Asymptotic behaviour of Bianchi VI(o) solutions with an exponential potential scalar field

Cited by in corpus (21)

• Dynamical systems applied to cosmology: dark energy and modified gravity
• Dynamical behavior in mimetic F(R) gravity
• A $\Lambda$CDM bounce scenario
• Bounce universe from string-inspired Gauss-Bonnet gravity
• Some remarks about non-minimally coupled scalar field models
• 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
• Anisotropic Spacetimes in Chiral Scalar Field Cosmology