Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation

Understand

We analyze the Bianchi I cosmology in the presence of a massless scalar field and describe its dynamics via a semiclassical and quantum polymer approach.

• We study the morphology of the Big Bounce by adopting three different sets of configurational variables: the Ashtekar connections, a set of anisotropic volume-like coordinates and the Universe volume plus two anisotropy coordinates (the latter two sets of variables would coincide in the case of an isotropic Universe).
• In the semiclassical analysis we demonstrate that the value of the critical matter energy density depends on the Cauchy problem for the dynamics when adopting the Ashtekar connections or the anisotropic volume-like coordinates.
• On the contrary, when the Universe volume is considered as a configurational coordinate, we are able to derive a polymer-modified Friedmann equation for the Bianchi I model, from which the expression of the critical energy density can be derived.