  We consider the introduction of anisotropy in a class of bouncing models of
cosmology. The presence of anisotropy often spells doom on bouncing models,
since the energy density due to the anisotropic stress outweighs that of other
matter components, as the universe contracts. Different suggestions have been
made in the literature to resolve this pathology, classically. Here, we
introduce a family of bouncing models, in which the shear density can be tuned
to either allow or forbid classical bouncing scenarios. Following this, we show
that quantum cosmological considerations can drastically change the above
scenario. Most importantly, we find that quantum effects can enable a bounce,
even when the anisotropic stress is large enough to forbid the same
classically. We employ the solutions of the appropriate mini-superspace
Wheeler-DeWitt equation for homogeneous, but anisotropic cosmologies, with the
boundary condition that the universe is initially contracting. Intriguingly,
the solution to the Wheeler-DeWitt equation exhibit an interesting phase
transition-like behaviour, wherein, the probability to have a bouncing universe
is precisely unity before the shear density reaches a critical value and then
starts to decrease abruptly as the shear density increases further. We verified
our findings using the tools of the Lorentzian quantum cosmology, along with
the application of the Picard-Lefschetz theory. In particular, the
semi-classical probability for a bounce has been re-derived from the imaginary
component of the on-shell effective action, evaluated at the complex saddle
points. Implications and future directions have also been discussed.
