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

Dark energy cosmologies with an equation-of-state parameter $w$ less than -1 are often found to violate the null energy condition and show unstable behaviour. A solution to this problem requires the existence of a consistent effective theory that violates the null energy condition only momentarily and does not develop any instabilities or other pathological features for the late-time cosmology. A model which incorporates a dynamical scalar field $\phi$ coupled to the quadratic Riemann invariant of the Gauss-Bonnet form is a viable proposal. Such an effective theory admits non-singular solutions for a wide range of scalar-Gauss-Bonnet coupling. The model also provides a reasonable explanation to the transition from matter dominance to dark energy regime and the late-time cosmic acceleration, offering an interesting testing ground for investigations of the cosmological modified gravity.