AbstractIn this work, we present a brief review of the branch‐cut cosmology as well as we approach topics not yet investigated. Starting with an already explored topic, the theme of the primordial singularity suppression, we approach essential themes for a better understanding of the scope of branch‐cut cosmology. More precisely, based on recent contributions, we advance a better understanding of the branch‐cut scenarios 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.