  We investigate cosmological scenarios containing one canonical scalar field
with an exponential potential in the context of bouncing models, where the
bounce happens due to quantum cosmological effects. The only possible bouncing
solutions in this scenario (discarding an infinitely fine tuned exception) must
have one and only one dark energy phase, either occurring in the contracting
era or in the expanding era. Hence,these bounce solutions are necessarily
asymmetric. We calculate the spectral indexes and amplitudes of scalar and
tensor perturbations numerically, considering the whole history of the model,
including the bounce phase itself, without making any approximation or using
any matching condition on the perturbations. As the background model is
necessarily dust dominated in the far past, the usual adiabatic vacuum initial
conditions can be easily imposed in this era. Hence, this is a cosmological
model where the presence of dark energy behavior in the Universe does not turn
problematic the usual vacuum initial conditions prescription for cosmological
perturbation in bouncing models. Scalar and tensor perturbations end up being
almost scale invariant, as expected. The background parameters can be adjusted,
without fine tunings, to yield the observed amplitude for scalar perturbations,
and also for the ratio between tensor and scalar amplitudes, $r = T/S \lesssim
0.1$. The amplification of scalar perturbations over tensor perturbations takes
place only around the bounce, due to quantum effects, and it would not occur if
General Relativity has remained valid throughout this phase. Hence, this is a
bouncing model where a single field induces not only an expanding background
dark energy phase, but also produces all observed features of cosmological
perturbations of quantum mechanical origin at linear order.
