Fermions in Loop Quantum Cosmology and the Role of Parity

TL;DR

This paper explores how fermions and parity violation influence the quantum cosmological models in loop quantum cosmology, especially affecting the nature of the big bang transition and the role of torsion.

Contribution

It introduces fermions and gravitational torsion into loop quantum cosmology, highlighting the impact of parity violation on the quantum dynamics of the universe.

Findings

Fermions prevent large matter contributions due to the exclusion principle.

Parity violation affects the microscopic structure of the big bang transition.

Wave functions are generally neither parity-even nor odd, influencing quantum cosmological models.

Abstract

Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it is not possible to avoid strong quantum regimes by positing a large matter content. Moreover, possible parity violating effects are important especially in loop quantum cosmology whose basic object is a difference equation for the wave function of the universe defined on a discrete space of triads. The two orientations of a triad are interchanged by a parity transformation, which leaves the difference equation invariant for ordinary matter. Here, we revisit and extend loop quantum cosmology by introducing fermions and the gravitational torsion they imply, which renders the parity issue non-trivial. A treatable locally rotationally symmetric Bianchi model is introduced which clearly shows the role of parity. General wave functions cannot be parity-even or odd, and parity violating effects in matter influence the microscopic big bang transition which replaces the classical singularity in loop quantum cosmology.