Future dynamics in f(R) theories

Abstract

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without invoking dark energy matter component. However, the freedom in the choice of the functional forms of $f(R)$ gives rise to the problem of how to constrain and break the degeneracy among these gravity theories on theoretical and/or observational grounds. In this paper to proceed further with the investigation on the potentialities, difficulties and limitations of $f(R)$ gravity, we examine the question as to whether the future dynamics can be used to break the degeneracy between $f(R)$ gravity theories by investigating the future dynamics of spatially homogeneous and isotropic dust flat models in two $f(R)$ gravity theories, namely the well known $f(R)=R+\alpha R^n$ gravity and another by A. Aviles et al., whose motivation comes from the cosmographic approach to $f(R)$ gravity. To this end we perform a detailed numerical study of the future dynamic of these flat model in these theories taking into account the recent constraints on the cosmological parameters made by the Planck team. We show that besides being powerful for discriminating between $f(R)$ gravity theories, the future dynamics technique can also be used to determine the fate of the Universe in the framework of these $f(R)$ gravity theories. Moreover, there emerges from our numerical analysis that if we do not invoke a dark energy component with equation-of-state parameter $\omega <-1$ one still has dust flat FLRW solution with a big rip, if gravity deviates from general relativity via $f(R)=R+\alpha R^n$. We also show that FLRW dust solutions with $f^{\prime \prime }<0$ do not necessarily lead to singularity.

12 pages, 8 figures. V2: Generality and implications of the results are emphasized, connection with the recent literature improved, typos corrected, references added

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• Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Effects of Spatial Curvature on the $f(R)$ Gravity Phase Space: no Inflationary Attractor?
• Autonomous Dynamical System Approach for Inflationary Gauss-Bonnet Modified Gravity
• A Study of Finite-time Singularities of Loop Quantum Cosmology Interacting Multifluids
• Autonomous Dynamical System of Einstein-Gauss-Bonnet Cosmologies
• The Classical and Loop Quantum Cosmology Phase Space of Interacting Dark Energy and Superfluid Dark Matter
• Autonomous Dynamical System Description of de Sitter Evolution in Scalar Assisted $f(R)-\varphi$ Gravity
• Modified gravity with an exponential function of curvature
• The Phase Space of $k$-Essence $f(R)$ Gravity Theory
• Phase Space description of Nonlocal Teleparallel Gravity
• Revisiting The Coincidence Problem in $f(R)$ Gravitation
• Generalized Logarithmic Equation of State in Classical and Loop Quantum Cosmology Dark Energy-Dark Matter Coupled Systems
• Cosmography and the redshift drift in Palatini $f(\mathcal{R})$ theories
• Perturbative solutions of the $f(R)$-theory of gravity in a central gravitational field and some applications
• A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity
• Pure geometric $f(R)$ branes