Bouncing with shear: Implications from quantum cosmology

Abstract

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.