Growth of covariant perturbations in the contracting phase of a bouncing
  universe
  In this paper we examine the validity of the linear perturbation theory near
a bounce in the covariant analysis. Some linearity parameters are defined to
set up conditions for a linear theory. Linear evolution of density perturbation
and gravitational waves have been computed previously. We have calculated the
vector and scalar induced parts of the shear tensor. For radiationlike and
dustlike single fluid dominated collapsing Friedmann-Lemaitre-Robertson-Walker
background it is shown that the linearity conditions are not satisfied near a
bounce.
