Cosmological "Ground State" Wave Functions in Gravity and Electromagnetism

TL;DR

This paper explores the connection between quantum cosmology solutions in gravity and electromagnetism, highlighting how certain solutions are artifacts of homogeneity assumptions, with implications for understanding the universe's ground states.

Contribution

It demonstrates the coincidence of quantum cosmology solutions in gravity and electromagnetism and clarifies the role of homogeneity in these solutions.

Findings

Quantum cosmology solutions in gravity and electromagnetism are coincident under certain conditions.

The coincidence is an artifact of homogeneity in cosmological space.

Electromagnetic solutions differ when homogeneity assumptions are relaxed.

Abstract

The coincidence of quantum cosmology solutions generated by solving a Euclidean version of the Hamilton-Jacobi equation for gravity and by using the complex canonical transformation of the Ashtekar variables is discussed. An examination of similar solutions for the free electromagnetic field shows that this coincidence is an artifact of the homogeneity of the cosmological space. (This paper will appear in a festchrift volume for Jerzy Plebanski)