On the stability of the cosmological solutions in f(R,G) gravity

Abstract

Modified gravity is one of the most promising candidates for explaining the current accelerating expansion of the Universe, and even its unification with the inflationary epoch. Nevertheless, the wide range of models capable to explain the phenomena of dark energy, imposes that current research focuses on a more precise study of the possible effects of modified gravity may have on both cosmological and local levels. In this paper, we focus on the analysis of a type of modified gravity, the so-called f(R,G) gravity and we perform a deep analysis on the stability of important cosmological solutions. This not only can help to constrain the form of the gravitational action, but also facilitate a better understanding of the behavior of the perturbations in this class of higher order theories of gravity, which will lead to a more precise analysis of the full spectrum of cosmological perturbations in future.

30 pages, 15 figures. Figures and conclusions improved, references added. Version to be published in Classical and Quantum Gravity

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• Dynamics of Inflation and Dark Energy from $F(R,\mathcal{G})$ Gravity
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• Finite-time Cosmological Singularities and the Possible Fate of the Universe
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• Reconstruction of $\Lambda$CDM Universe in $f(Q)$ Gravity
• Unification of a Bounce with a Viable Dark Energy Era in Gauss-Bonnet Gravity
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
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• Big Bang Nucleosynthesis constraints on higher-order modified gravities
• Gravastars in $f(R,G)$ Gravity
• De Sitter solutions in Einstein-Gauss-Bonnet gravity
• Crossing phantom divide in $f(Q)$ gravity
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• Reconstruction of Scalar Potentials in Modified Gravity Models
• An Axially Symmetric Transitioning models with Observational Constraints
• Inflationary magnetogenesis with reheating phase from higher curvature coupling
• The Raychaudhuri equation in homogeneous cosmologies
• f(Lovelock) theories of gravity
• Focusing of geodesic congruences in an accelerated expanding Universe
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• Bouncing cosmology in $f(R,\mathcal{G})$ gravity by order reduction
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• Observational Constraints and Cosmographic Analysis of $f(T,T_G)$ Gravity and Cosmology
• Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity
• Cosmological Tests of $f(R,G,T)$ Dark Energy Model in FRW Universe
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• Exploring cosmological evolution and constraints in $f(T)$ teleparallel gravity
• Constructions of $f(R,G,\mathcal{T})$ Gravity from Some Expansions of the Universe
• Parametrizing the transition to the phantom epoch with Supernovae Ia and Standard Rulers
• Ensemble Average Theory of Gravity
• Complete density perturbations in the Jordan-Fierz-Brans-Dicke theory
• Squared torsion $f(T,\mathcal{T})$ gravity and its cosmological implications
• Bulk viscous matter in $f(T)$ gravity: A path to cosmic acceleration
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• How a conformally flat (GR)4 impacts Gauss-Bonnet gravity?
• Late-time Cosmology of scalar field assisted $f(\mathcal{G})$ gravity
• Collapsing scenarios of K-essence generalized Vaidya spacetime under $f(\bar{R},\bar{T})$ gravity
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• Energy Conditions in Gauss-Bonnet Gravity
• Gödel-type solutions within the $f(R,Q,P)$ gravity
• Extended Bose-Einstein condensate dark matter in viscous Gauss-Bonnet gravity
• Stable $f(Q)$ gravity model through non-trivial connection
• Isotropic universe with almost scale-invariant fourth-order gravity
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• Backreaction mechanism in multifluid and extended cosmologies
• The Fate of the Universe Evolution in the Quadratic Form of Ricci-Gauss-Bonnet Cosmology
• Parameterized Deceleration in $f(Q,C)$ Gravity: A Logarithmic Approach
• Dynamics of Potentials in Bianchi Type Scalar-Tensor Cosmology
• On 1 + 3 covariant perturbations of the quasi-Newtonian space-time in modified Gauss-Bonnet gravity
• Non-minimal scalar-tensor theories
• Impact of projective curvature tensor in $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_m\right)$-gravity
• Mass gap in non-perturbative quadratic ${\mathcal{R}}^2$ gravity via Dyson-Schwinger
• Dark Energy Behavior from Static Equation of State in Non-Minimally Coupled Gravity with Scalar Deformation
• $f(R,\mathcal{G})$-cosmological dynamics in the FLRW background
• Cosmology in the mimetic higher-curvature $f(R,R_{\mu \nu }{R}^{\mu \nu })$ gravity
• Generalized Noether Theorem for Gauss-Bonnet Cosmology