Singularities in Cosmological Loop Correlators II : Non Local Interactions and Flat Space limits
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| Format: | Preprint |
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2025
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| author | Ansari, Elaf Bhowmick, Supritha Ghosh, Diptimoy |
| author_facet | Ansari, Elaf Bhowmick, Supritha Ghosh, Diptimoy |
| contents | Non-local interactions naturally arise in the ADM formalism after solving the constraint equations and substituting their solutions back into the action. However, the effects of these non-local operators on loop corrections to cosmological correlators remain largely unexplored. Extending the analysis of arXiv:2503.21880 , in this work we compute the $1$-loop bispectrum during slow-roll inflation, including the inverse-Laplacian operators present at cubic and quartic order in the ADM action (in the spatially flat gauge). These non-local vertices introduce non-trivial angular dependencies that significantly complicate the evaluation of loop integrals. We find that the diagrammatic rules of arXiv:2503.21880 for identifying poles and branch cuts in correlators without explicit integration remain valid even in the presence of such non-local interactions. Finally, we derive the flat-space limit of the $1$-loop inflationary correlator and verify it with explicit examples, thereby establishing a direct correspondence between its leading total-energy singularities ($ω_T\rightarrow0$) and the flat-space scattering amplitude. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_11040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularities in Cosmological Loop Correlators II : Non Local Interactions and Flat Space limits Ansari, Elaf Bhowmick, Supritha Ghosh, Diptimoy High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Non-local interactions naturally arise in the ADM formalism after solving the constraint equations and substituting their solutions back into the action. However, the effects of these non-local operators on loop corrections to cosmological correlators remain largely unexplored. Extending the analysis of arXiv:2503.21880 , in this work we compute the $1$-loop bispectrum during slow-roll inflation, including the inverse-Laplacian operators present at cubic and quartic order in the ADM action (in the spatially flat gauge). These non-local vertices introduce non-trivial angular dependencies that significantly complicate the evaluation of loop integrals. We find that the diagrammatic rules of arXiv:2503.21880 for identifying poles and branch cuts in correlators without explicit integration remain valid even in the presence of such non-local interactions. Finally, we derive the flat-space limit of the $1$-loop inflationary correlator and verify it with explicit examples, thereby establishing a direct correspondence between its leading total-energy singularities ($ω_T\rightarrow0$) and the flat-space scattering amplitude. |
| title | Singularities in Cosmological Loop Correlators II : Non Local Interactions and Flat Space limits |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.11040 |