The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology

Abstract

In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include non-linear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semi-classical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising from the inclusion of anisotropies. We show that the anisotropic shear term grows during the collapsing phase, but remains finite through the bounce. Immediately following the bounce, the anisotropies decay and with the inclusion of matter with equation of state $w < +1$, the universe isotropizes in the expanding phase.