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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05422 |
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| _version_ | 1866914025622732800 |
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| author | Leonard, William Ortolá Slepian, Zachary |
| author_facet | Leonard, William Ortolá Slepian, Zachary |
| contents | Analytical templates for the 4-Point Correlation Function (4PCF) covariance matrix have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the second part of the beyond GRF calculation of the 4PCF covariance, incorporating 1-loop corrections stemming from the third-order density contrast. Furthermore, we introduce a non-trivial galaxy biasing scheme at third order. To simplify the calculation, we decompose the covariance into three distinct structures and leverage the isotropic basis of Cahn & Slepian (2023). This approach reduces the complexity of the high-dimensional integrals that would be 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 our ability to probe both its parity-even and parity-odd modes. This is the second and final paper in a two-part series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05422 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm II}$: 1-Loop Corrections with Third-Order Densities Leonard, William Ortolá Slepian, Zachary Cosmology and Nongalactic Astrophysics Analytical templates for the 4-Point Correlation Function (4PCF) covariance matrix have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the second part of the beyond GRF calculation of the 4PCF covariance, incorporating 1-loop corrections stemming from the third-order density contrast. Furthermore, we introduce a non-trivial galaxy biasing scheme at third order. To simplify the calculation, we decompose the covariance into three distinct structures and leverage the isotropic basis of Cahn & Slepian (2023). This approach reduces the complexity of the high-dimensional integrals that would be 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 our ability to probe both its parity-even and parity-odd modes. This is the second and final paper in a two-part series. |
| title | Analytical Template for the 4-Point Correlation Function Covariance Beyond the Gaussian Random Field ${\rm II}$: 1-Loop Corrections with Third-Order Densities |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2509.05422 |