Cosmology meets cohomology
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929511329693696 |
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| author | De, Shounak Pokraka, Andrzej |
| author_facet | De, Shounak Pokraka, Andrzej |
| contents | The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated \emph{relative} twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03753 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cosmology meets cohomology De, Shounak Pokraka, Andrzej High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Algebraic Geometry The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated \emph{relative} twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators. |
| title | Cosmology meets cohomology |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2308.03753 |