Energy conditions in modified Gauss-Bonnet gravity

In considering alternative higher-order gravity theories, one is liable to be motivated in pursuing models consistent and inspired by several candidates of a fundamental theory of quantum gravity. Indeed, motivations from string/$\mathrm{M}$ theory predict that scalar field couplings with the Gauss-Bonnet invariant, $G$, are important in the appearance of nonsingular early time cosmologies. In this work, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity or $f(G)$ gravity. We consider specific realistic forms of $f(G)$ analyzed in the literature that account for the late-time cosmic acceleration and that have been found to cure the finite-time future singularities present in the dark energy models. We present the general inequalities imposed by the energy conditions and use the recent estimated values of the Hubble, deceleration, jerk and snap parameters to examine the viability of the above-mentioned forms of $f(G)$ imposed by the weak energy condition.

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