Extending the solutions and the equations of quantum gravity past the big bang singularity

TL;DR

This paper demonstrates that solutions to quantum gravity equations near the big bang can be extended past the singularity using symmetric mirroring of eigenfunctions, providing insights into the early universe and antimatter.

Contribution

It introduces a method to extend quantum gravity solutions beyond the big bang singularity using eigenfunction symmetry, advancing understanding of early universe models.

Findings

Eigenfunctions can be extended past the singularity via even or odd mirroring.

Extended solutions are smooth and satisfy the equations in the classical sense.

The approach offers an explanation for the missing antimatter in the universe.

Abstract

In [8] we recently proved that in our model of quantum gravity the solutions to the quantized version of the full Einstein equations or to the Wheeler-DeWitt equation could be expressed as products of spatial and temporal eigenfunctions, or eigendistributions, of self-adjoint operators acting in corresponding separable Hilbert spaces. Moreover, near the big bang singularity we derived sharp asymptotic estimates for the temporal eigenfunctions. In this paper we show that, by using these estimates, there exists a complete sequence of unitarily equivalent eigenfunctions which can be extended past the singularity by even or odd mirroring as sufficiently smooth functions such that the extended functions are solutions of the appropriately extended equations valid in $\R[]$ in the classical sense. We also use this phenomenon to explain the missing antimatter.