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Large-scale modeling of the observed power spectrum multipoles

Robin Y. Wen1,*, Henry S. Grasshorn Gebhardt1,2, Chen Heinrich1, and Olivier Doré1,2

  • *Contact author: ywen@caltech.edu
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Phys. Rev. D 114, 043502 – Published 3 August, 2026

DOI: https://doi.org/10.1103/mbqc-f3cf

Abstract

Current and upcoming large-scale structure surveys are pushing toward increasingly wide angular coverage, where wide-angle effects—arising from the varying line of sight across the curved sky—become critical for accurate modeling of the three-dimensional galaxy power spectrum. At the same time, these survey’s broader redshift reach makes the effects of redshift evolution—beyond the effective-redshift approximation—non-negligible on large radial scales. Additional observational effects such as the survey window function and integral constraints also become significant on these large scales, necessitating a careful theoretical treatment to robustly constrain local primordial non-Gaussianities and relativistic effects. In this work, we present a consistent and accurate theoretical framework for modeling the commonly used power spectrum multipoles (PSM) on large scales using the discrete spherical Fourier-Bessel (dSFB) basis. This basis ensures numerical stability and allows an exact separation between angular and radial modes. Using the dSFB basis, we study the impact of wide-angle effects and redshift evolution on the PSM, and incorporate the effects of window function convolution and integral constraints. We validate our PSM modeling using lognormal mocks under radial integral constraints with realistic survey geometries, demonstrating the readiness of our framework for application to all-sky galaxy surveys.

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References (97)

  1. DESI Collaboration, J. Cosmol. Astropart. Phys. 07 (2025) 017 .
  2. Euclid Collaboration, Astron. Astrophys. 697, A1 (2025).
  3. J. J. Bock (SPHEREx Collaboration), Astrophys. J. 999, 139 (2026).
  4. N. Kaiser, Mon. Not. R. Astron. Soc. 227, 1 (1987).
  5. A. J. S. Hamilton, Astrophys. J. Lett. 385, L5 (1992).
  6. K. Yamamoto, M. Nakamichi, A. Kamino, B. A. Bassett, and H. Nishioka, Publ. Astron. Soc. Jpn. 58, 93 (2006).
  7. F. Beutler, H.-J. Seo, S. Saito et al., Mon. Not. R. Astron. Soc. 466, 2242 (2017).
  8. E. Castorina, N. Hand, U. Seljak et al., J. Cosmol. Astropart. Phys. 09 (2019) 010.
  9. G. d’Amico, J. Gleyzes, N. Kokron, K. Markovic, L. Senatore, P. Zhang, F. Beutler, and H. Gil-Marín, J. Cosmol. Astropart. Phys. 05 (2020) 005.
  10. M. M. Ivanov, M. Simonović, and M. Zaldarriaga, J. Cosmol. Astropart. Phys. 05 (2020) 042.
  11. F. Beutler and P. McDonald, J. Cosmol. Astropart. Phys. 11 (2021) 031.
  12. DESI Collaboration, J. Cosmol. Astropart. Phys. 09 (2025) 008.
  13. E. Chaussidon, C. Yèche, A. de Mattia et al., J. Cosmol. Astropart. Phys. 06 (2025) 029.
  14. A. S. Szalay, T. Matsubara, and S. D. Landy, Astrophys. J. Lett. 498, L1 (1998).
  15. J. Yoo and U. Seljak, Mon. Not. R. Astron. Soc. 447, 1789 (2015).
  16. E. Castorina and M. White, Mon. Not. R. Astron. Soc. 476, 4403 (2018).
  17. M. Noorikuhani and R. Scoccimarro, Phys. Rev. D 107, 083528 (2023).
  18. J. N. Benabou, I. Sands, H. S. Grasshorn Gebhardt, C. Heinrich, and O. Doré, Phys. Rev. D 110, 083526 (2024).
  19. R. Y. Wen, H. S. Grasshorn Gebhardt, C. Heinrich, and O. Doré, Phys. Rev. D 110, 083525 (2024).
  20. L. Samushia, arXiv:1906.05866.
  21. H. S. Grasshorn Gebhardt and O. Doré, Phys. Rev. D 104, 123548 (2021).
  22. R. Y. Wen, H. S. Grasshorn Gebhardt, C. Heinrich, and O. Doré, Phys. Rev. D 110, 123501 (2024).
  23. J. A. Peacock and D. Nicholson, Mon. Not. R. Astron. Soc. 253, 307 (1991).
  24. A. de Mattia and V. Ruhlmann-Kleider, J. Cosmol. Astropart. Phys. 08 (2019) 036.
  25. E. Castorina and E. Di Dio, J. Cosmol. Astropart. Phys. 01 (2022) 061.
  26. H. S. Grasshorn Gebhardt and O. Doré, Phys. Rev. D 109, 083502 (2024).
  27. B. Leistedt, H. V. Peiris, and J. D. McEwen, in Wavelets and Sparsity XV, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, edited by D. Van De Ville, V. K. Goyal, and M. Papadakis (2013), Vol. 8858, p. 88580J.
  28. B. Leistedt, J. D. McEwen, T. D. Kitching, and H. V. Peiris, Phys. Rev. D 92, 123010 (2015).
  29. J. E. Campagne, J. Neveu, and S. Plaszczynski, Astron. Astrophys. 602, A72 (2017).
  30. S. Chiarenza, M. Bonici, W. Percival, and M. White, Open J. Astrophys. 7, 112 (2024).
  31. Planck Collaboration VI, Astron. Astrophys. 641, A6 (2020).
  32. A. Raccanelli, L. Samushia, and W. J. Percival, Mon. Not. R. Astron. Soc. 409, 1525 (2010).
  33. J. Yoo, Phys. Rev. D 82, 083508 (2010).
  34. A. Challinor and A. Lewis, Phys. Rev. D 84, 043516 (2011).
  35. C. Bonvin and R. Durrer, Phys. Rev. D 84, 063505 (2011).
  36. D. Jeong, F. Schmidt, and C. M. Hirata, Phys. Rev. D 85, 023504 (2012).
  37. N. Grimm, F. Scaccabarozzi, J. Yoo, S. G. Biern, and J.-O. Gong, J. Cosmol. Astropart. Phys. 11 (2020) 064.
  38. F. Scaccabarozzi, J. Yoo, and S. G. Biern, J. Cosmol. Astropart. Phys. 10 (2018) 024.
  39. R. Scoccimarro, Phys. Rev. D 92, 083532 (2015).
  40. D. Bianchi, H. Gil-Marín, R. Ruggeri, and W. J. Percival, Mon. Not. R. Astron. Soc.: Lett. 453, L11 (2015).
  41. F. Beutler, E. Castorina, and P. Zhang, J. Cosmol. Astropart. Phys. 03 (2019) 040.
  42. N. Hand, Y. Li, Z. Slepian, and U. Seljak, J. Cosmol. Astropart. Phys. 07 (2017) 002.
  43. B. Khek, H. G. Gebhardt, and O. Doré, Phys. Rev. D 110, 063524 (2024).
  44. R. Y. Wen, H. S. G. Gebhardt, C. Heinrich, and O. Doré, Phys. Rev. D 112, 063518 (2025).
  45. P. Reimberg, F. Bernardeau, and C. Pitrou, J. Cosmol. Astropart. Phys. 01 (2016) 048.
  46. P. Paul, C. Clarkson, and R. Maartens, J. Cosmol. Astropart. Phys. 04 (2023) 067.
  47. E. Castorina and M. White, Mon. Not. R. Astron. Soc. 499, 893 (2020).
  48. I. Szapudi, Astrophys. J. 614, 51 (2004).
  49. P. Pápai and I. Szapudi, Mon. Not. R. Astron. Soc. 389, 292 (2008).
  50. J. E. Campagne, S. Plaszczynski, and J. Neveu, Astrophys. J. 845, 28 (2017).
  51. V. Tansella, C. Bonvin, R. Durrer, B. Ghosh, and E. Sellentin, J. Cosmol. Astropart. Phys. 03 (2018) 019.
  52. M. Foglieni, M. Pantiri, E. Di Dio, and E. Castorina, Phys. Rev. Lett. 131, 111201 (2023).
  53. C. Bonvin, F. Lepori, S. Schulz, I. Tutusaus, J. Adamek, and P. Fosalba, Mon. Not. R. Astron. Soc. 525, 4611 (2023).
  54. D. S. Blanco, C. Bonvin, C. Clarkson, and R. Maartens, J. Cosmol. Astropart. Phys. 12 (2024) 029.
  55. A. Raccanelli and Z. Vlah, arXiv:2305.16278.
  56. A. Raccanelli and Z. Vlah, Phys. Rev. D 108, 043537 (2023).
  57. F. Spezzati, E. Vanzan, A. Raccanelli, Z. Vlah, and D. Bertacca, Phys. Rev. D 112, 023530 (2025).
  58. A. Obuljen and W. J. Percival, J. Cosmol. Astropart. Phys. 11 (2021) 006.
  59. D. Wadekar and R. Scoccimarro, Phys. Rev. D 102, 123517 (2020).
  60. K. B. Fisher, O. Lahav, Y. Hoffman et al., Mon. Not. R. Astron. Soc. 272, 885 (1995).
  61. E.-M. Mueller, M. Rezaie, W. J. Percival et al., Mon. Not. R. Astron. Soc. 514, 3396 (2022).
  62. M. S. Cagliari, E. Castorina, M. Bonici, and D. Bianchi, J. Cosmol. Astropart. Phys. 08 (2024) 036.
  63. H. A. Feldman, N. Kaiser, and J. A. Peacock, Astrophys. J. 426, 23 (1994).
  64. A. Taruya, T. Nishimichi, and D. Jeong, Phys. Rev. D 103, 023501 (2021).
  65. E. Hivon, K. M. Górski, C. B. Netterfield, B. P. Crill, S. Prunet, and F. Hansen, Astrophys. J. 567, 2 (2002).
  66. D. Alonso, J. Sanchez, A. Slosar (LSST Dark Energy Science Collaboration), Mon. Not. R. Astron. Soc. 484, 4127 (2019).
  67. S. Alam, M. Ata, S. Bailey et al., Mon. Not. R. Astron. Soc. 470, 2617 (2017).
  68. Y.-K. Chiang, Astrophys. J. 958, 118 (2023).
  69. E. F. Schlafly, A. M. Meisner, and G. M. Green, Astrophys. J. Suppl. Ser. 240, 30 (2019).
  70. A. J. Ross, W. J. Percival, A. G. Sánchez et al., Mon. Not. R. Astron. Soc. 424, 564 (2012).
  71. H. S. Grasshorn Gebhardt and O. Doré, J. Cosmol. Astropart. Phys. 01 (2022) 038.
  72. S. Everett, B. Yanny, N. Kuropatkin et al., Astrophys. J. Suppl. Ser. 258, 15 (2022).
  73. H. Kong, A. J. Ross, K. Honscheid et al., J. Cosmol. Astropart. Phys. 01 (2025) 146.
  74. D. Anbajagane, M. Tabbutt, J. Beas-Gonzalez et al., Open J. Astrophys. 8, 65 (2025).
  75. D. Alonso and P. G. Ferreira, Phys. Rev. D 92, 063525 (2015).
  76. D. Contreras, M. C. Johnson, and J. B. Mertens, J. Cosmol. Astropart. Phys. 10 (2019) 024.
  77. C. Bonvin, F. Lepori, S. Schulz, I. Tutusaus, J. Adamek, and P. Fosalba, Mon. Not. R. Astron. Soc. 525, 4611 (2023).
  78. J. M. Sullivan and U. Seljak, Phys. Rev. D 112, 083522 (2025).
  79. N. Dalal and W. J. Percival, J. Cosmol. Astropart. Phys. 04 (2026) 037.
  80. A. Barreira, J. Cosmol. Astropart. Phys. 12 (2020) 031.
  81. A. Barreira, J. Cosmol. Astropart. Phys. 11 (2022) 013.
  82. J. M. Sullivan, T. Prijon, and U. Seljak, J. Cosmol. Astropart. Phys. 08 (2023) 004.
  83. A. Barreira and E. Krause, J. Cosmol. Astropart. Phys. 10 (2023) 044.
  84. C. Zhao, C.-H. Chuang, J. Bautista et al., Mon. Not. R. Astron. Soc. 503, 1149 (2021).
  85. P. J. E. Peebles, Astrophys. J. 185, 413 (1973).
  86. F. Beutler, S. Saito, H.-J. Seo et al., Mon. Not. R. Astron. Soc. 443, 1065 (2014).
  87. Euclid Collaboration, M. Y. Elkhashab, D. Bertacca et al., Astron. Astrophys. 697, A85 (2025).
  88. M. J. Wilson, J. A. Peacock, A. N. Taylor, and S. de la Torre, Mon. Not. R. Astron. Soc. 464, 3121 (2017).
  89. R. Neveux, E. Burtin, A. de Mattia et al., Mon. Not. R. Astron. Soc. 499, 210 (2020).
  90. J. Hou, A. G. Sánchez, A. J. Ross et al., Mon. Not. R. Astron. Soc. 500, 1201 (2021).
  91. E.-M. Mueller, M. Rezaie, W. J. Percival et al., Mon. Not. R. Astron. Soc. 514, 3396 (2022).
  92. L. C. Maximon, J. Math. Phys. (N.Y.) 32, 642 (1991).
  93. R. Mehrem, arXiv:1908.07374.
  94. O. H. E. Philcox and Z. Slepian, Phys. Rev. D 103, 123509 (2021).
  95. C. Bonvin, L. Hui, and E. Gaztañaga, Phys. Rev. D 89, 083535 (2014).
  96. E. Castorina and M. White, Mon. Not. R. Astron. Soc. 479, 741 (2018).
  97. M. A. Al-Gwaiz, Sturm-Liouville Theory and its Applications (Springer, New York, 2008), Vol. 264.

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Phys. Rev. D 114, 043502– Published 3 August, 2026
  • Received 27 January 2026
  • Accepted 10 July 2026
Article part of CHORUS
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