Loop Quantum Cosmology of Bianchi I Model in $\barμ$ and $\barμ'$ Schemes with Higher Order Holonomy Corrections
The detailed formulation of loop quantum cosmology with higher order holonomy corrections has been constructed recently in the homogeneous and isotropic spacetime, yet it is important to extend the higher order holonomy corrections to include the effects of anisotropy which typically grow during the collapsing phase. In this paper we investigate the Bianchi I model in $\barμ$ and $\barμ'$ schemes respectively. First we construct the effective dynamics with higher order holonomy corrections in a massless scalar field, then we extend it to the inclusion of an arbitrary matter. Besides that, we also analyze the behavior of the anisotropy during the evolution of the universe. We find that as in the isotropic case, the singularity is never approached and the quantum bounces are generic, regardless of the order of the holonomy corrections. Some differences in the bouncing phase of the two schemes are also found out. It is also shown that in the two schemes the behavior of the anisotropy is not the same before and after the bounces.