O(d,d)-invariance in inhomogeneous string cosmologies with perfect fluid
  In the first part of the present paper, we show that O(d,d)-invariance usually known in a homogeneous cosmological background written in terms of proper time can be extended to backgrounds depending on one or several coordinates (which may be any space-like or time-like coordinate(s)). In all cases, the presence of a perfect fluid is taken into account and the equivalent duality transformation in Einstein frame is explicitly given. In the second part, we present several concrete applications to some four-dimensional metrics, including inhomogeneous ones, which illustrate the different duality transformations discussed in the first part. Note that most of the dual solutions given here do not seem to be known in the literature. 
Jacques Demaret and Elisa Di Pietro