Large-scale homogeneity and isotropy versus fine-scale condensation: A model based on Muckenhoupt-type densities

Authors

  • Hugo Aimar Instituto de Matemática Aplicada del Litoral, UNL, CONICET. CCT CONICET Santa Fe, Predio “Dr. Alberto Cassano”, Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
  • Federico Morana Instituto de Matemática Aplicada del Litoral, UNL, CONICET. CCT CONICET Santa Fe, Predio “Dr. Alberto Cassano”, Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina

DOI:

https://doi.org/10.33044/revuma.3670

Abstract

In this brief note we aim to provide, through a well-known class of singular densities in harmonic analysis, a simple approach to the fact that the homogeneity of the universe on scales of the order of a hundred million light years is entirely compatible with the fine-scale condensation of matter and energy. We give precise and quantitative definitions of homogeneity and isotropy on large scales. Then we show that Muckenhoupt densities have the ingredients required for a model of the large-scale homogeneity and the fine-scale condensation of the universe. In particular, these densities can take locally infinitely large values (black holes) and, at the same time, they are independent of location at large scales. We also show some locally singular densities that satisfy the large-scale isotropy property.

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References

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Published

2025-03-29

Issue

Vol. 68 No. 1 (2025)

Section

Article

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Copyright (c) 2025 Hugo Aimar, Federico Morana

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