An Exact Fermionic Chern-Simons-Kodama State in Quantum Gravity

TL;DR

This paper constructs an exact fermionic extension of the Chern-Simons-Kodama state in quantum gravity, revealing new solutions that incorporate fermions and torsion, with implications for cosmology and singularity avoidance.

Contribution

It introduces a generalized fermionic CSK state solving extended Hamiltonian constraints exactly, linking it to cosmological wave functions and singularity resolution.

Findings

Reduces to original Kodama state in symmetric limits

Incorporates fermionic and torsion effects

Potential to evade Big Bang singularity

Abstract

The Chern-Simons-Kodama (CSK) state is an exact, non-perturbative wave function in the Ashtekar formulation of classical General Relativity. In this work, we find a generalized fermionic CSK state by solving the extended gravitational and fermionic Hamiltonian constraints of the Wheeler-DeWitt equation exactly. We show that this new state reduces to the original Kodama state upon symmetry reduction to FRW coordinates with perturbative fermionic corrections, making contact with the Hartle-Hawking and Vilenkin wave functions of the universe in cosmology. We also find that when both torsion and fermions are non-vanishing, the wave function possesses a finite amplitude to evade the Big Bang curvature singularity.