# Behavior of the Universe anisotropy in a big-bounce cosmology

## TL;DR

This paper explores how a polymer quantum approach to Bianchi I cosmology with stiff matter removes the classical singularity, replacing it with a Big-Bounce, and shows anisotropies remain finite through this transition, suggesting a generic cosmological model.

## Contribution

It introduces a polymer quantum framework for Bianchi I models that eliminates the Big-Bang singularity and controls anisotropies, extending to Bianchi IX as a generic scenario.

## Key findings

- Big-Bounce replaces classical singularity in the model.
- Anisotropies remain finite and well-behaved across the bounce.
- The approach can be extended to Bianchi IX cosmology.

## Abstract

We investigate the classical and quantum behavior of a Bianchi I model in the presence of a stiff matter contribution when the Vilenkin interpretation of the wave function of the Universe is taken into account. We study its evolution in the so-called polymer representation of quantum mechanics, in order to characterize the modifications that a discrete nature in the isotropic variable of the Universe induces on the morphology of the cosmological singularity. We demonstrate that in such a model the Big-Bang singularity is removed at a semiclassical level in favor of a Big-Bounce when a lattice on the isotropic variable is considered. Furthermore, the analysis of the mean values on the quantum degrees of freedom, \textit{i.e} the variables $\beta_{+},\beta_{-}$ in the Misner picture, and the investigation on the evolution of the wave packets show how the typical diverging behavior associated to the anisotropies of the Universe in proximity of the initial singularity disappears in our polymer modified scheme. Indeed, the anisotropies remain finite across the Big-Bounce and they assume a value that depends on the initial conditions fixed far from the turning point. Finally, we demonstrate that the proposed scenario can be extended, with a suitable choice of the configuration parameters, to the Bianchi IX cosmology and therefore it can be regarded as a paradigm for the generic cosmological model.