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http://hdl.handle.net/2289/8668| Title: | Quantum cosmology as a hydrogen atom: discrete Λ and cyclic universes from Wheeler–DeWitt quantization |
| Authors: | Mukherjee, Dipayan Sahota, Harkirat Singh Shankaranarayanan, S |
| Issue Date: | 9-Feb-2026 |
| Publisher: | Classical and Quantum Gravity |
| Citation: | Classical and Quantum Gravity, 2026, Vol. 43 (3), AR No. 035015 |
| Abstract: | Building upon our recently established correspondence between quantum cosmology and the hydrogen atom (Sahota et al 2025 arXiv:2505.16863 [gr-qc]), we investigate the specific sector of a negative cosmological constant (Λ < 0) in a flat FLRW Universe with dust. While the positive Λ sector (Sahota et al 2025 arXiv:2505.16863 [gr-qc]) yields a continuous spectrum and a single bounce, we show here that the negative Λ sector leads to a discrete spectrum of energy eigenvalues, effectively quantizing the cosmological constant. Within this dual description, the operatorordering ambiguity parameter appears as the azimuthal quantum number of the hydrogen atom. A skewed Bohr correspondence emerges for the bound states, matching classical evolution at large volumes but deviating near the bounce. By constructing wave packets from these bound states, we demonstrate that the classical Big Bang and Big Crunch singularities are resolved, and the Universe oscillates between quantum bounces and classical turnaround points. The expectation values of the observables indicate a cyclic Universe—with vanishing Hubble parameter at turnarounds undergoing quantum bounces. This exactly solvable model offers a tractable setting to explore quantum gravitational effects in cosmology. We analyze the properties of this cyclic Universe, contrasting its bound-state dynamics with the scattering states of the de Sitter case. |
| Description: | Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations) |
| URI: | http://hdl.handle.net/2289/8668 |
| ISSN: | 1361-6382 |
| Alternative Location: | https://doi.org/10.48550/arXiv.2601.20286 http://dx.doi.org/10.1088/1361-6382/ae3e4b |
| Copyright: | 2026 IOP Publishing Ltd. |
| Appears in Collections: | Research Papers (A&A) |
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| 2026_Classical and Quantum Gravity_Vol. 43 (3)_AR No. 035015.pdf Restricted Access | Restricted Access | 652.71 kB | Adobe PDF | View/Open Request a copy |
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