  The scale factor duality is a symmetry of dilaton gravity which is known to
lead to pre-big-bang cosmologies. A conformal time version of the scale factor
duality (SFD) was recently implemented as a UV/IR symmetry between decelerated
and accelerated phases of the post-big-bang evolution within Einstein gravity
coupled to a scalar field. The problem investigated in the present paper
concerns the employment of the conformal time SFD methods to the construction
of pre-big-bang and cyclic extensions of these models. We demonstrate that each
big-bang model gives rise to two qualitatively different pre-big-bang
evolutions: a contraction/expansion SFD model and Penrose's Conformal Cyclic
Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving
certain gauged K\"ahler sigma models minimally coupled to Einstein gravity are
studied. We also describe the specific SFD features of the thermodynamics and
the conditions for validity of the generalized second law in the case of
Gauss-Bonnet (GB) extension of these selected CCC models.
