Sourced fluctuations in generic slow contraction
  We introduce a set of generic conditions for the slow contracting Universe
and for a narrowed-down category of models called fast-roll models. We present
general conditions for super horizon freeze-out of scalar and tensor
perturbations and show that any fast-roll model satisfies them, as in the case
of inflation. We are interested in the "Sourced Bounce" scenario, where
perturbations are sourced by a $U(1)$ gauge field coupled to a bouncer scalar
field. The requirement of a slightly red tilted scalar spectrum greatly
restricts the allowed couplings between the scalar and the gauge field. We show
that a viable slightly red scalar spectrum is achievable. However, within the
fast-roll approximation, the tensor-to-scalar ratio is in general $r\simeq
1/9$, inconsistent with current observations. We demonstrate the general result
with an explicit example we dub "Intermediate contraction". We prove that small
modifications in fast-roll that do not alter the Green's functions do not
result in $r<0.06$ consistent with the data for more than an e-fold. Hence, a
successful "Sourced Bounce" requires a different source or a significant
deviation from fast-roll.
