Perturbative Unitarity and the Wavefunction of the Universe
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2023
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| author | Albayrak, Soner Benincasa, Paolo Pueyo, Carlos Duaso |
| author_facet | Albayrak, Soner Benincasa, Paolo Pueyo, Carlos Duaso |
| contents | Unitarity of time evolution is one of the basic principles constraining physical processes. Its consequences in the perturbative Bunch-Davies wavefunction in cosmology have been formulated in terms of the cosmological optical theorem. In this paper, we re-analyse perturbative unitarity for the Bunch-Davies wavefunction, focusing on: 1) the role of the $iε$-prescription and its compatibility with the requirement of unitarity; 2) the origin of the different "cutting rules"; 3) the emergence of the flat-space optical theorem from the cosmological one. We take the combinatorial point of view of the cosmological polytopes, which provide a first-principle description for a large class of scalar graphs contributing to the wavefunctional. The requirement of the positivity of the geometry together with the preservation of its orientation determine the $iε$-prescription. In kinematic space it translates into giving a small negative imaginary part to all the energies, making the wavefunction coefficients well-defined for any value of their real part along the real axis. Unitarity is instead encoded into a non-convex part of the cosmological polytope, which we name optical polytope. The cosmological optical theorem emerges as the equivalence between a specific polytope subdivision of the optical polytope and its triangulations, each of which provides different cutting rules. The flat-space optical theorem instead emerges from the non-convexity of the optical polytope. On the more mathematical side, we provide two definitions of this non-convex geometry, none of them based on the idea of the non-convex geometry as a union of convex ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19686 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perturbative Unitarity and the Wavefunction of the Universe Albayrak, Soner Benincasa, Paolo Pueyo, Carlos Duaso High Energy Physics - Theory General Relativity and Quantum Cosmology Combinatorics Unitarity of time evolution is one of the basic principles constraining physical processes. Its consequences in the perturbative Bunch-Davies wavefunction in cosmology have been formulated in terms of the cosmological optical theorem. In this paper, we re-analyse perturbative unitarity for the Bunch-Davies wavefunction, focusing on: 1) the role of the $iε$-prescription and its compatibility with the requirement of unitarity; 2) the origin of the different "cutting rules"; 3) the emergence of the flat-space optical theorem from the cosmological one. We take the combinatorial point of view of the cosmological polytopes, which provide a first-principle description for a large class of scalar graphs contributing to the wavefunctional. The requirement of the positivity of the geometry together with the preservation of its orientation determine the $iε$-prescription. In kinematic space it translates into giving a small negative imaginary part to all the energies, making the wavefunction coefficients well-defined for any value of their real part along the real axis. Unitarity is instead encoded into a non-convex part of the cosmological polytope, which we name optical polytope. The cosmological optical theorem emerges as the equivalence between a specific polytope subdivision of the optical polytope and its triangulations, each of which provides different cutting rules. The flat-space optical theorem instead emerges from the non-convexity of the optical polytope. On the more mathematical side, we provide two definitions of this non-convex geometry, none of them based on the idea of the non-convex geometry as a union of convex ones. |
| title | Perturbative Unitarity and the Wavefunction of the Universe |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Combinatorics |
| url | https://arxiv.org/abs/2305.19686 |