Vector perturbations in bouncing cosmology
  An old question surrounding bouncing models concerns their stability under
vector perturbations. Considering perfect fluids or scalar fields, vector
perturbations evolve kinematically as $a^{-2}$, where $a$ is the scale factor.
Consequently, a definite answer concerning the bounce stability depends on an
arbitrary constant, therefore, there is no definitive answer. In this paper, we
consider a more general situation where the primeval material medium is a
non-ideal fluid, and its shear viscosity is capable of producing torque
oscillations, which can create and dynamically sustain vector perturbations
along cosmic evolution. In this framework, one can set that vector
perturbations have a quantum mechanical origin, coming from quantum vacuum
fluctuations in the far past of the bouncing model, as it is done with scalar
and tensor perturbations. Under this prescription, one can calculate their
evolution during the whole history of the bouncing model, and precisely infer
the conditions under which they remain linear before the expanding phase. It is
shown that such linearity conditions impose constraints on the free parameters
of bouncing models, which are mild, although not trivial, allowing a large
class of possibilities. Such conditions impose that vector perturbations are
also not observationally relevant in the expanding phase. The conclusion is
that bouncing models are generally stable under vector perturbations. As they
are also stable under scalar and tensor perturbations, we conclude that
bouncing models are generally stable under perturbations originated from
quantum vacuum perturbations in the far past of their contracting phase.
