  In Pre-Big-Bang and in Ekpyrotic Cosmology, perturbations on cosmological
scales today are generated from quantum vacuum fluctuations during a phase when
the Universe is contracting (viewed in the Einstein frame). The backgrounds
studied to date do not yield a scale invariant spectrum of adiabatic
fluctuations. Here, we present a new contracting background model (neither of
Pre-Big-Bang nor of the Ekpyrotic form) involving a single scalar field coupled
to gravity in which a scale-invariant spectrum of curvature fluctuations and
gravitational waves results. The equation of state of this scalar field
corresponds to cold matter. We demonstrate that if this contracting phase can
be matched via a nonsingular bounce to an expanding Friedmann cosmology, the
scale-invariance of the curvature fluctuations is maintained. We also find new
background solutions for Pre-Big-Bang and for Ekpyrotic cosmology, which
involve two scalar fields with exponential potentials with background values
which are evolving in time. We comment on the difficulty of obtaining a
scale-invariant spectrum of adiabatic fluctuations with background solutions
which have been studied in the past.
