  We demonstrate, by a simple analysis, that cosmological line elements related
by scale factor duality also exhibit a duality with respect to the
conservation/violation of the Weak Energy Condition (WEC) by the matter that
acts as the source in the one-loop beta function equations for the metric
coupling written explicitly in the form of the Einstein equations. Furthermore,
a study of specific pairs of line elements (obtained via O(d,d)
transformations) hints at a possible generalisation of the above duality w.r.t.
WEC for the case of O(d,d) related spacetimes. Consequences and extensions
thereof are also pointed out.
