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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2603.16776 |
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| _version_ | 1866918395765587968 |
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| author | Takeuchi, Tsutomu T. |
| author_facet | Takeuchi, Tsutomu T. |
| contents | The cosmic dipole in galaxy number counts is traditionally described by the Ellis--Baldwin (EB) formula under simplifying assumptions of power-law source counts and flux-limited selection. We reformulate the EB dipole as a symmetry response of observed counts to a Lorentz boost, leading to the general expression $D=βR$, where $R=\partial\ln N/\partial\lnβ$ encodes the underlying population and selection effects. The classical EB formula is recovered as a limiting case. We show that this response framework extends beyond one-point statistics: Lorentz boosts induce a dipole component in the two-point correlation function and, more generally, a hierarchy of responses in $n$-point statistics. We further clarify the relation to redshift-space distortions and relativistic galaxy clustering, and provide a unified description in which observer- and source-induced dipoles contribute to the same multipole component. This establishes the cosmic dipole as a symmetry response of finite-sample point-process statistics, offering a new perspective on dipole anisotropies and their observational interpretation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16776 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cosmic Dipole as a Symmetry Response: From the Ellis--Baldwin Formula to Correlation Function Dipoles Takeuchi, Tsutomu T. Cosmology and Nongalactic Astrophysics The cosmic dipole in galaxy number counts is traditionally described by the Ellis--Baldwin (EB) formula under simplifying assumptions of power-law source counts and flux-limited selection. We reformulate the EB dipole as a symmetry response of observed counts to a Lorentz boost, leading to the general expression $D=βR$, where $R=\partial\ln N/\partial\lnβ$ encodes the underlying population and selection effects. The classical EB formula is recovered as a limiting case. We show that this response framework extends beyond one-point statistics: Lorentz boosts induce a dipole component in the two-point correlation function and, more generally, a hierarchy of responses in $n$-point statistics. We further clarify the relation to redshift-space distortions and relativistic galaxy clustering, and provide a unified description in which observer- and source-induced dipoles contribute to the same multipole component. This establishes the cosmic dipole as a symmetry response of finite-sample point-process statistics, offering a new perspective on dipole anisotropies and their observational interpretation. |
| title | Cosmic Dipole as a Symmetry Response: From the Ellis--Baldwin Formula to Correlation Function Dipoles |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2603.16776 |