Combining gravity with the forces of the standard model on a cosmological scale

TL;DR

This paper establishes a spectral resolution for the Wheeler-DeWitt equation in a cosmological setting with combined gravitational and standard model forces, highlighting complex eigenfunction structures when electro-weak interactions are included.

Contribution

It proves the existence of a spectral resolution for the Wheeler-DeWitt equation in a Friedman universe with standard model forces, extending previous work to include electro-weak interactions.

Findings

Spectral resolution exists for the Wheeler-DeWitt equation in this setting.

Eigenfunctions involving electro-weak interactions are generally not one-dimensional.

The wave functions map to a subspace of the antisymmetric Fock space.

Abstract

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the underlying spacetime is a Friedman universe with flat spatial slices and where the matter fields are comprised of the strong interaction, with $\SU(3)$ replaced by a general $\SU(n)$, $n\ge 2$, and the electro-weak interaction. The wave functions are maps from $\R[4n+10]$ to a subspace of the antisymmetric Fock space, and one noteworthy result is that, whenever the electro-weak interaction is involved, the image of an eigenfunction is in general not one dimensional, i.e., in general it makes no sense specifying a fermion and looking for an eigenfunction the range of which is contained in the one dimensional vector space spanned by the fermion.