Polymer Bianchi-I with polymer matter
arXiv:2509.24586
The paper investigates the effective dynamics of a Bianchi‑I universe where both the geometry and a scalar field are polymer‑quantized, using a dust field as an internal clock, and derives an effective Friedmann equation showing how different polymer scales alter cosmological evolution and the quantum bounce.
Abstract
We analyze the effective dynamics of a polymer quantized Bianchi-I universe coupled to a polymer quantized scalar field, with a pressureless dust field acting as an internal clock. We show 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 further derive an effective Friedmann equation for this model, and compute the shear scalar. We find that polymer quantizing the scalar field leads to significant differences in the evolution of various cosmological quantities as compared to standard quantization. The amount of these variations, as well as the location of the quantum bounce, depends on the matter polymer scale.
v2: 33 pages, 15 figures; Results and discussion pertaining to asymmetry have been removed, as it was an issue with the numerics. Main results and calculations remain unchanged. A new subsection highlighting differences between polymerized and standard scalar field added. Additional minor changes, corrections, and some clarifying discussion added