  Assuming that curvature perturbations and gravitational waves originally
arise from vacuum fluctuations in a matter-dominated phase of contraction, we
study the dynamics of the cosmological perturbations evolving through a
nonsingular bouncing phase described by a generic single scalar field
Lagrangian minimally coupled to Einstein gravity. In order for such a model to
be consistent with the current upper limits on the tensor-to-scalar ratio,
there must be an enhancement of the curvature fluctuations during the bounce
phase. We show that, while it remains possible to enlarge the amplitude of
curvature perturbations due to the nontrivial background evolution, this growth
is very limited because of the conservation of curvature perturbations on
super-Hubble scales. We further perform a general analysis of the evolution of
primordial non-Gaussianities through the bounce phase. By studying the general
form of the bispectrum we show that the non-Gaussianity parameter
$f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced
during the bounce phase if the curvature fluctuations grow. Hence, in such
nonsingular bounce models with matter given by a single scalar field, there
appears to be a tension between obtaining a small enough tensor-to-scalar ratio
and not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upper
bounds. This conclusion may be considered as a "no-go" theorem that rules out
any single field matter bounce cosmology starting with vacuum initial
conditions for the fluctuations.
