Extending solutions and the equations of quantum gravity past the big bang singularity - Gerhardt, Claus (Symmetry, 2025)
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.