Marcelo Marzola The Branch-Cut Cosmology: evidences and open questions César A. Zen Vasconcellos, Peter O. Hess, José de Freitas Pacheco, Dimiter Hadjimichef, Benno Bodmann Hide abstract | Show figures | Show BibTeX | Show discussion | View PDF | 2212.03825v1 In this work we present a brief summary of the branch-cut cosmology as well as we approach topics not yet explored. Starting with an already explored topic, the theme of primordial singularity suppression, we approach for the first time essential themes for a better understanding of the scope of branch-cut cosmology. Based on recent contributions, we advance a better understanding of the scenarios revealed in these formulations as well as essential topics for modern cosmology such as the flatness, homogeneity and horizon problems from the classical point of view of the branch-cut cosmology. Authors' comments: Astronomische Nachrichten, 2023. arXiv admin note: text overlap with arXiv:2212.02670. text overlap with arXiv:1803.01961 by other authors