  In recent years different explanations are provided for both an inflation and
a recent acceleration in the expansion of the universe. In this Letter we show
that a model of physical interest is the modification of general relativity
with a Gauss-Bonnet term coupled to a dynamical scalar-field as predicted by
certain versions of string theory. This construction provides a model of
evolving dark energy that naturally explains a dynamical relaxation of the
vacuum energy (gravitationally repulsive potential) to a small value
(exponentially close to zero) after a sufficient number of e-folds. The model
also leads to a small deviation from the $w=-1$ prediction of non-evolving dark
energy.
