Quantum Gravity, de Sitter Space, and Normalizability
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| Format: | Preprint |
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2025
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| _version_ | 1866915604717371392 |
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| author | Alexander, Stephon Bernardo, Heliudson Kuntzleman, Jacob Pezzelle, Max |
| author_facet | Alexander, Stephon Bernardo, Heliudson Kuntzleman, Jacob Pezzelle, Max |
| contents | We propose a resolution to the longstanding problem of perturbative normalizability in canonical quantum gravity of the Lorentzian Chern-Simons-Kodama (CSK) state with a positive cosmological constant in four dimensions. While the CSK state is an exact solution to the Hamiltonian constraint in the self-dual formulation and semiclassically describes de Sitter spacetime, its physical viability has been questioned due to apparent nonnormalizability and CPT asymmetry. Starting from a nonperturbative holomorphic inner product derived from the reality conditions of the self-dual Ashtekar variables, we show that the linearization, in terms of gravitons, of the CSK state is perturbatively normalizable for super-Planckian cosmological constant. Furthermore, we demonstrate that a rotation in phase space, a generalization of Thiemann's complexifier, can render the full perturbative state normalizable for all $Λ$ by analytically continuing the non-convergent modes in phase space. This provides the first concrete realization of a CPT-breaking, yet normalizable, gravitational vacuum state rooted in a nonperturbative quantum gravity framework. Our results establish the CSK state-long thought formal-as a viable candidate for the ground state of quantum gravity in de Sitter space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_05417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Gravity, de Sitter Space, and Normalizability Alexander, Stephon Bernardo, Heliudson Kuntzleman, Jacob Pezzelle, Max High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We propose a resolution to the longstanding problem of perturbative normalizability in canonical quantum gravity of the Lorentzian Chern-Simons-Kodama (CSK) state with a positive cosmological constant in four dimensions. While the CSK state is an exact solution to the Hamiltonian constraint in the self-dual formulation and semiclassically describes de Sitter spacetime, its physical viability has been questioned due to apparent nonnormalizability and CPT asymmetry. Starting from a nonperturbative holomorphic inner product derived from the reality conditions of the self-dual Ashtekar variables, we show that the linearization, in terms of gravitons, of the CSK state is perturbatively normalizable for super-Planckian cosmological constant. Furthermore, we demonstrate that a rotation in phase space, a generalization of Thiemann's complexifier, can render the full perturbative state normalizable for all $Λ$ by analytically continuing the non-convergent modes in phase space. This provides the first concrete realization of a CPT-breaking, yet normalizable, gravitational vacuum state rooted in a nonperturbative quantum gravity framework. Our results establish the CSK state-long thought formal-as a viable candidate for the ground state of quantum gravity in de Sitter space. |
| title | Quantum Gravity, de Sitter Space, and Normalizability |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.05417 |