Interacting fluids generating identical, dual and phantom cosmologies

We find the group of symmetry transformations generated by interacting fluids in spatially flat Friedmann-Robertson-Walker (FRW) spacetime which links cosmologies with the same scale factor (identity) or with scale factors a and a−1 (duality). There exists a duality between contracting and superaccelerated expanding scenarios associated with (phantom) cosmologies. We investigate the action of this symmetry group on self-interacting minimally (conformally) coupled quintessence and k-essence cosmologies.