Skip to Main Content

Access Provided by Xinjiang University

Physical Review D

Access by Xinjiang University

Homogeneity scale in the local Universe: Model-independent estimate from S-PLUS iDR6 blue galaxies

Camila Franco ^*, Felipe Avila ^†, Armando Bernui ^‡, and E. Telles

Ulisses Ribeiro and Clécio R. Bom^§

Arianna Cortesi

C. Mendes de Oliveira

Observatório Nacional, Rua General José Cristino, 77, São Cristóvão, 20921-400, Rio de Janeiro, Rio de Janeiro, Brazil

Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil

Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, Brazil and Observatório do Valongo, Ladeira Pedro Antonio, 43, 20080-090, Rio de Janeiro, Brazil

The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, California 91101, USA

Rubin Observatory Project Office, 950 North Cherry Avenue, Tucson, Arizona 85719, USA

Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, Santa Catarina 88040-900, Brazil

Universidade de São Paulo, IAG, Rua do Matão 1225, São Paulo, São Paulo, Brazil

^*Contact author: camilafranco@on.br
^†Contact author: felipeavila@on.br
^‡Contact author: bernui@on.br
^§Contact author: debom@cbpf.br

Phys. Rev. D 114, 083504 – Published 5 October, 2026

DOI: https://doi.org/10.1103/382j-p22b

Abstract

We present a model-independent estimate of the angular homogeneity scale in the local Universe by analyzing data from the Southern Photometric Local Universe Survey (S-PLUS). Two complementary estimators are employed: (i) a parametric approach fitting the power-law of the two-point angular correlation function, which yields the homogeneity scale $θ_{H} = 8.9 4_{- 3.38}^{+ 1.20} \deg$ ; and (ii) a nonparametric fractal correlation dimension method, computing $D_{2} (θ)$ directly from the correlation function, which results in $θ_{H} = 7.9 1_{- 2.94}^{+ 5.50} \deg$ . We apply both methodologies to a set of mock catalogs, generated with the Generator for Large Scale Structure algorithm, and find that both estimates are well within $1 σ$ of their respective median values. The transition scale to homogeneity, according to the $Λ$ cold dark matter (CDM) model, is defined for matter, i.e., $b = 1$ . Measurements of this scale with observational data clearly depend on the cosmic tracer analyzed, and a calibration is necessary. Our study with blue galaxies, with bias $b ≃ 1$ , provides a suitable estimate for comparison. Indeed, the results obtained in both approaches are compared with the value expected in the $Λ CDM$ model, obtaining a good concordance.

Physics Subject Headings (PhySH)

Large scale structure of the Universe

Article Text

References (87)

K. Bolejko and J. S. B. Wyithe, J. Cosmol. Astropart. Phys. 02 (2009) 020
R. Maartens, Proc. R. Soc. A 369, 5115 (2011).
H. Fujii, Serb. Astron. J. 204, 29 (2022), https://ui.adsabs.harvard.edu/abs/2022SerAJ.204...29F/abstract.
R. S. Gonçalves, G. C. Carvalho, C. A. P. Bengaly, J. C. Carvalho, and J. S. Alcaniz, Mon. Not. R. Astron. Soc. 481, 5270 (2018).
N. J. Secrest, S. von Hausegger, M. Rameez, R. Mohayaee, S. Sarkar, and J. Colin, Astrophys. J. Lett. 908, L51 (2021).
P. K. Aluri and P. Jain, Mon. Not. R. Astron. Soc. 419, 3378 (2012).
M. I. Khan and R. Saha, J. Cosmol. Astropart. Phys. 06 (2022) 006.
C. P. Novaes, A. Bernui, G. A. Marques, and I. S. Ferreira, Mon. Not. R. Astron. Soc. 461, 1363 (2016).
Planck Collaboration, Astron. Astrophys. 641, A7 (2020).
G. A. Marques, C. P. Novaes, A. Bernui, and I. S. Ferreira, Mon. Not. R. Astron. Soc. 473, 165 (2018).
G. Galloni, N. Bartolo, S. Matarrese, M. Migliaccio, A. Ricciardone, and N. Vittorio, J. Cosmol. Astropart. Phys. 09 (2022) 046.
M. Lopes, A. Bernui, W. S. Hipólito-Ricaldi, C. Franco, and F. Avila, Astron. Astrophys. 694, A77 (2025).
J. Řípa and A. Shafieloo, Mon. Not. R. Astron. Soc. 486, 3027 (2019).
D. Alonso, A. Bueno Belloso, F. J. Sánchez, J. García-Bellido, and E. Sánchez, Mon. Not. R. Astron. Soc. 440, 10 (2014).
S. Appleby and A. Shafieloo, J. Cosmol. Astropart. Phys. 10 (2014) 070
F. Avila, C. P. Novaes, A. Bernui, E. de Carvalho, and J. P. Nogueira-Cavalcante, Mon. Not. R. Astron. Soc. 488, 1481 (2019).
H. M. Courtois, D. Pomarède, R. B. Tully, Y. Hoffman, and D. Courtois, Astron. J. 146, 69 (2013).
R. S. Gonçalves, G. C. Carvalho, C. A. P. Bengaly, Jr., J. C. Carvalho, A. Bernui, J. S. Alcaniz, and R. Maartens, Mon. Not. R. Astron. Soc. 475, L20 (2018).
S. Sarkar, B. Pandey, and R. Khatri, Mon. Not. R. Astron. Soc. 483, 2453 (2019).
M. I. Scrimgeour et al., Mon. Not. R. Astron. Soc. 425, 116 (2012).
F. Sylos Labini and Y. V. Baryshev, J. Cosmol. Astropart. Phys. 06 (2010) 021
Z. Chang, D. Zhao, and Y. Zhou, Chin. Phys. C 43, 125102 (2019).
M. Lopes, A. Bernui, C. Franco, and F. Avila, Astrophys. J. 967, 47 (2024).
R. Mokeddem, M. Lopes, F. Avila, A. Bernui, and W. S. Hipólito-Ricaldi, Phys. Dark Universe 51, 102185 (2026).
L. Perivolaropoulos, Phys. Rev. D 108, 063509 (2023).
F. Avila, J. Oliveira, M. L. S. Dias, and A. Bernui, Braz. J. Phys. 53, 49 (2023).
B. B. Bizarria, C. P. Novaes, F. Avila, R. Mokeddem, H. H. da Costa, C. A. Wuensche, and G. A. S. Silva, Mon. Not. R. Astron. Soc. 548, stag771 (2026).
C. Franco, F. Avila, and A. Bernui, Mon. Not. R. Astron. Soc. 527, 7400 (2024).
Y.-W. Wu and J.-Q. Xia, Astrophys. J. 979, 3 (2025).
C. E. Kester, A. Bernui, and W. S. Hipólito-Ricaldi, Astron. Astrophys. 683, A176 (2024).
P. Kumar Aluri et al., Classical Quantum Gravity 40, 094001 (2023).
P. Laurent et al., J. Cosmol. Astropart. Phys. 11 (2016) 060.
F. Avila, A. Bernui, R. C. Nunes, E. de Carvalho, and C. P. Novaes, Mon. Not. R. Astron. Soc. 509, 2994 (2022).
R. S. Gonçalves, G. C. Carvalho, U. Andrade, C. A. P. Bengaly, J. C. Carvalho, and J. Alcaniz, J. Cosmol. Astropart. Phys. 03 (2021) 029
P. Ntelis et al., J. Cosmol. Astropart. Phys. 06 (2017) 019.
C. Clarkson, C. R. Phys. 13, 682 (2012).
F. Avila, C. P. Novaes, A. Bernui, and E. de Carvalho, J. Cosmol. Astropart. Phys. 12 (2018) 041.
P. Fanha, A. da Silva, J. Fonseca, J. P. Mimoso, and Z. Sakr, arXiv:2606.18975.
C. Mendes de Oliveira et al., Mon. Not. R. Astron. Soc. 489, 241 (2019).
F. R. Herpich et al., Astron. Astrophys. 689, A249 (2024).
G. B. O. Schwarz et al., Astron. Comput. 51, 100899 (2025).
D. J. Croton, P. Norberg, E. Gaztañaga, and C. M. Baugh, Mon. Not. R. Astron. Soc. 379, 1562 (2007).
F. G. Mohammad et al., Astron. Astrophys. 610, A59 (2018).
A. J. Ross et al., Mon. Not. R. Astron. Soc. 437, 1109 (2014).
I. Zehavi et al., Astrophys. J. 630, 1 (2005).
A. Dressler et al., Astrophys. J. 490, 577 (1997).
B. F. Gerke et al., Mon. Not. R. Astron. Soc. 376, 1425 (2007).
F. Avila, E. de Carvalho, A. Bernui, H. Lima, and R. C. Nunes, Mon. Not. R. Astron. Soc. 529, 4980 (2024).
E. de Carvalho, A. Bernui, F. Avila, C. P. Novaes, and J. P. Nogueira-Cavalcante, Astron. Astrophys. 649, A20 (2021).
S. P. Bamford et al., Mon. Not. R. Astron. Soc. 393, 1324 (2009).
U. Ribeiro et al., Phys. Rev. D 113, 043537 (2026).
L. Nakazono et al., Mon. Not. R. Astron. Soc. 507, 5847 (2021).
E. V. R. Lima et al., Astron. Comput. 38, 100510 (2022).
C. Bom et al., Mon. Not. R. Astron. Soc. 528, 4188 (2024).
J. S. Bagla, J. Yadav, and T. R. Seshadri, Mon. Not. R. Astron. Soc. 390, 829 (2008).
P. H. Coleman and L. Pietronero, Phys. Rep. 213, 311 (1992).
L. Pietronero, Physica (Amsterdam) 144A, 257 (1987).
J. K. Yadav, J. S. Bagla, and N. Khandai, Mon. Not. R. Astron. Soc. 405, 2009 (2010).
S. D. Landy and A. S. Szalay, Astrophys. J. 412, 64 (1993).
A. L. Coil, Planets, Stars and Stellar Systems. Volume 6: Extragalactic Astronomy and Cosmology, edited by T. D. Oswalt and W. C. Keel Springer, Dordrecht, 2013), Vol. 6, p. 387.
A. J. Connolly et al., Astrophys. J. 579, 42 (2002).
C. Franco, J. Oliveira, M. Lopes, F. Avila, and A. Bernui, Mon. Not. R. Astron. Soc. 537, 897 (2025).
H. Kurki-Suonio, Galaxy survey cosmology, https://www.mv.helsinki.fi/home/hkurkisu/GSC1.pdf (2023).
G. A. Marques and A. Bernui, J. Cosmol. Astropart. Phys. 05 (2020) 052.
P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, NJ, 1993).
H. Totsuji and T. Kihara, Publ. Astron. Soc. Jpn. 21, 221 (1969).
P. Virtanen et al., Nat. Methods 17, 261 (2020).
M. Jarvis, TreeCorr: Two-point correlation functions (2015).
N. Tessore, A. Loureiro, B. Joachimi, M. von Wietersheim-Kramsta, and N. Jeffrey, Open J. Astrophys. 6, 11 (2023).
L. Blot et al., Mon. Not. R. Astron. Soc. 485, 2806 (2019).
M. Colavincenzo et al., Mon. Not. R. Astron. Soc. 482, 4883 (2019).
M. Lippich et al., Mon. Not. R. Astron. Soc. 482, 1786 (2019).
M. Crocce, A. Cabré, and E. Gaztañaga, Mon. Not. R. Astron. Soc. 414, 329 (2011).
N. E. Chisari et al., Astrophys. J. Suppl. Ser. 242, 2 (2019).
A. Lewis and A. Challinor, CAMB: Code for anisotropies in the microwave background (2011).
Planck Collaboration, Astron. Astrophys. 641, A6 (2020).
L. Wasserman, All of Statistics: A Concise Course in Statistical Inference (Springer, New York, New York, NY, 2004).
U. Andrade, R. S. Gonçalves, G. C. Carvalho, C. A. P. Bengaly, J. C. Carvalho, and J. Alcaniz, J. Cosmol. Astropart. Phys. 10 (2022) 088.
J. Asorey, M. Carrasco Kind, I. Sevilla-Noarbe, R. J. Brunner, and J. Thaler, Mon. Not. R. Astron. Soc. 459, 1293 (2016).
H. M. Courtois, J. Mould, A. M. Hollinger, A. Dupuy, and C. P. Zhang, Astron. Astrophys. 701, A187 (2025).
M. Einasto, Mon. Not. R. Astron. Soc. 252, 261 (1991).
C. Franco, F. Avila, and A. Bernui, Astrophys. J. 993, 133 (2025).
S. Gavas, J. S. Bagla, and N. Khandai, Phys. Rev. D 111, 043516 (2025).
C. P. Novaes et al., Phys. Rev. D 111, 083510 (2025).
E. Telles and S. Maddox, Mon. Not. R. Astron. Soc. 311, 307 (2000).
D. Huterer, Astron. Astrophys. Rev. 31, 2 (2023).
J. N. Fry and E. Gaztanaga, Astrophys. J. 413, 447 (1993).