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Dark energy cosmologies with an equation of state parameter $w$ less than -1are often found to violate the null energy condition and show unstablebehaviour. A solution to this problem may require the existence of a consistenteffective theory that violates the null energy condition only momentarily anddoes not develop any instabilities or other pathological features for a latetime cosmology. A model which incorporates a dynamical scalar field $\phi$coupled to the quadratic Riemann invariant of the Gauss-Bonnet form is a viableproposal. Such an effective theory is shown to admit nonsingular cosmologicalevolutions for a wide range of scalar-Gauss-Bonnet coupling. We discuss theconditions for which our model yields observationally supported spectra ofscalar and tensor fluctuations, under cosmological perturbations. The model canprovide a reasonable explanation for the transition from matter dominance todark energy regime and the late time cosmic acceleration, offering aninteresting testing ground for investigations of the cosmological modifiedgravity.Comment: 44 pages, several eps figures; section 2 expanded with discussions on  cosmological/astrophysical constraints, final in JCA

Gauss–Bonnet cosmologies: crossing the phantom divide and the transition from matter dominance to dark energy