English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this brief note we aim to provide, through a well known class of singulardensities in harmonic analysis, a simple approach to the fact that thehomogeneity of the universe on scales of the order of a hundred millions lightyears is completely compatible with the fine-scale condensation of matter andenergy. We give precise and quantitative definitions of homogeneity andisotropy on large scales. Then we show that Muckenhoupt densities have theingredients required to a model for the large-scale homogeneity and thefine-scale condensation of the universe. In particular, these densities cantake locally infinitely large values (black holes) and at once, in the largescales they are independent of the location. We also show some locally singulardensities satisfying the large scale isotropy property.

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