Polymer Bianchi-I with polymer matter

Abstract

We analyze the effective dynamics of a polymer quantized homogeneous and anisotropic Bianchi-I universe coupled to a polymer quantized scalar field. We use a pressureless dust field as an internal clock, and work with the gravitational Misner variables. We find that for a consistent polymer quantization of the anisotropies, the volume variable has to be polymerized first, and that a choice of different polymer scales for the two leads to substantially different dynamics. We derive an effective Friedmann equation for this model, and also compute the shear scalar. We show that polymer quantizing the scalar field leads to significant differences in the evolution of various cosmological quantities as compared to standard quantization. Furthermore, there is asymmetric evolution across the bounce for both the volume variable and the anisotropies. The amount of these variations and asymmetry, as well as the location of the quantum bounce, depends on the matter polymer scale.