Phase space of modified Gauss-Bonnet gravity

Abstract

We investigate the evolution of non vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the the emergence of accelerated expansion. As in $f(R)$ gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.

13 pages, 5 figures, 1 table

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• Dynamical systems of modified Gauss-Bonnet gravity: cosmological implications
• New class of generalized coupling theories
• Cosmological Evolution of Two-Scalar fields Cosmology in the Jordan frame
• Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory
• Dynamical reconstruction of the $\Lambda$CDM model in scalar-tensor $f(R,T)$ gravity
• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• Gravitational waves in Modified Gauss-Bonnet Gravity
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• New cosmological solutions in hybrid metric-Palatini gravity from dynamical symmetries
• Gauss-Bonnet Gravity in $D=4$ Without Gauss-Bonnet Coupling to Matter - Cosmological Implications
• $\Lambda$CDM-like evolution in Einstein-scalar-Gauss-Bonnet gravity
• Correspondence between particle creation and dark components interaction in the context of $f(\mathcal{G})$ gravity