{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T03:00:40Z","timestamp":1774580440975,"version":"3.50.1"},"reference-count":11,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T00:00:00Z","timestamp":1739059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2013DeWitt 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.<\/jats:p>","DOI":"10.3390\/sym17020262","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T06:43:07Z","timestamp":1739169787000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Extending Solutions and the Equations of Quantum Gravity Past the Big Bang Singularity"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1328-1457","authenticated-orcid":false,"given":"Claus","family":"Gerhardt","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Ruprecht-Karls-Universit\u00e4t, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.4310\/ATMP.2013.v17.n6.a5","article-title":"The quantization of gravity in globally hyperbolic spacetimes","volume":"17","author":"Gerhardt","year":"2013","journal-title":"Adv. Theor. Math. Phys."},{"key":"ref_2","unstructured":"Witten, L. (1962). The Dynamics of General Relativity, John Wiley. Gravitation: An introduction to current research."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gerhardt, C. (2024). The Quantization of Gravity, Springer. [2nd ed.]. Fundamental Theories of Physics.","DOI":"10.1007\/978-3-031-67922-3"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gerhardt, C. (2021). The quantization of gravity: Quantization of the Hamilton equations. Universe, 7.","DOI":"10.3390\/universe7040091"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gerhardt, C. (2023). The quantization of gravity: The quantization of the full Einstein equations. Symmetry, 15.","DOI":"10.3390\/sym15081599"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Gerhardt, C. (2022). A unified quantization of gravity and other fundamental forces of nature. Universe, 8.","DOI":"10.3390\/universe8080404"},{"key":"ref_7","unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Handbook of Mathematical Functions, Cambridge University Press. (In English)."},{"key":"ref_8","unstructured":"Teubner, S. (1983). Gew\u00f6hnliche Differentialgleichungen, Teubner. [10th ed.]. (In German)."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Courant, R., and Hilbert, D. (1968). Methoden der Mathematischen Physik. I, Springer. Dritte Auflage, Heidelberger Taschenb\u00fccher, Band 30.","DOI":"10.1007\/978-3-662-00844-7"},{"key":"ref_10","unstructured":"Maurin, K. (1967). Methods of Hilbert Spaces, Pa\u0144stwowe Wydawnictwo Naukowe. Translated from the Polish by Andrzej Alexiewicz and Waclaw Zawadowski; Monografie Matematyczne."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gerhardt, C. (2025). Extending the Solutions and the Equations of Quantum Gravity Past the Big Bang Singularity. arXiv.","DOI":"10.3390\/sym17020262"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/262\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:29:54Z","timestamp":1760027394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/262"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,9]]},"references-count":11,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020262"],"URL":"https:\/\/doi.org\/10.3390\/sym17020262","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,9]]}}}