Quantum Mixmaster as a Model of the Primordial Universe

The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for the early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl–Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in the numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined.

CLASSICAL AND QUANTUM FEATURES OF THE MIXMASTER SINGULARITY

This review paper is devoted to analyzing the main properties of the cosmological singularity associated with the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in detail the main results obtained over the last forty years on the Mixmaster topic. We first assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and the quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.

MIXMASTER DYNAMICS IN THE WHEELER-DEWITT FRAMEWORK

In this work we present an analysis of the Mixmaster model in the Wheeler-DeWitt framework. After a brief review of the classical evolution, several aspects of the semi-classical and of the quantum dynamics are discussed: the most important results we will present are a possible operator ordering obtained from the semi-classical analysis and the full characterization of the quantum dynamics in Misner-Chitré like variables.