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 may require 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 a late time cosmology. A model which incorporates a dynamical scalar field φ coupled to the quadratic Riemann invariant of the Gauss–Bonnet form is a viable proposal. Such an effective theory is shown to admit non-singular cosmological evolutions for a wide range of scalar–Gauss–Bonnet coupling. We discuss the conditions for which our model yields observationally supported spectra of scalar and tensor fluctuations, under cosmological perturbations. The model can provide a reasonable explanation for 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.
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A 2007 study studied this question.