Behavior of Bianchi type I spacetime by path integral approach in LQC

Abstract

We investigate the expansion behavior of Bianchi type I spacetime with a massless scalar field and a cosmological constant using the path integral approach of loop quantum cosmology developed by Ashtekar, Campiglia, and Henderson [Phys. Rev. D 82, 124043 (2010)]. We obtain the effective action for this model and calculate the semiclassical solutions. Although classical general relativity is a good approximation at large scales, it is shown that the loop quantum effect induces a repulsive force at small scales to avoid the big bang singularity as in the isotropic cases. We investigate the evolution of anisotropy in detail and find that the anisotropy cannot increase indefinitely like in the classical case.