  We implement a conformal time scale factor duality for
Friedmann-Robertson-Walker cosmological models, which is consistent with the
weak energy condition. The requirement for self-duality determines the
equations of state for a broad class of barotropic fluids. We study the example
of a universe filled with two interacting fluids, presenting an accelerated and
a decelerated period, with manifest UV/IR duality. The associated self-dual
scalar field interaction turns out to coincide with the "radiation-like"
modified Chaplygin gas models. We present an equivalent realization of them as
gauged K\"ahler sigma models (minimally coupled to gravity) with very specific
and interrelated K\"ahler- and super-potentials. Their applications in the
description of hilltop inflation and also as quintessence models for the late
universe are discussed.
