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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.05419 |
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| _version_ | 1866911140656709632 |
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| author | Leonard, William Ortolá Slepian, Zachary |
| author_facet | Leonard, William Ortolá Slepian, Zachary |
| contents | Analytical templates for the covariance matrix of the 4-Point Correlation Function (4PCF) have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the first non-Gaussian calculation of the 4PCF covariance, incorporating 1-loop corrections using the second-order density contrast. Furthermore, we introduce a non-trivial galaxy bias scheme at second order. To simplify the calculation, we decompose the covariance into five distinct structures, and then exploit the isotropic basis functions of Cahn & Slepian (2023). This approach reduces the complexity of the high-dimensional integrals naively involved, enabling the angular parts to be performed and leaving us with low-dimensional radial integrals. This analytical template will provide a more accurate characterization of the statistical errors on the 4PCF, improving both the parity-odd and parity-even analyses. This is the first paper in a two-part series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm I}$: 1-Loop Corrections involving Second-Order Densities Leonard, William Ortolá Slepian, Zachary Cosmology and Nongalactic Astrophysics Analytical templates for the covariance matrix of the 4-Point Correlation Function (4PCF) have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the first non-Gaussian calculation of the 4PCF covariance, incorporating 1-loop corrections using the second-order density contrast. Furthermore, we introduce a non-trivial galaxy bias scheme at second order. To simplify the calculation, we decompose the covariance into five distinct structures, and then exploit the isotropic basis functions of Cahn & Slepian (2023). This approach reduces the complexity of the high-dimensional integrals naively involved, enabling the angular parts to be performed and leaving us with low-dimensional radial integrals. This analytical template will provide a more accurate characterization of the statistical errors on the 4PCF, improving both the parity-odd and parity-even analyses. This is the first paper in a two-part series. |
| title | Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm I}$: 1-Loop Corrections involving Second-Order Densities |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2509.05419 |