On the Conceptual Limits of Conformal Cyclic Cosmology

Conformal Cyclic Cosmology (CCC), proposed by Roger Penrose, o ers an elegant geo metric solution to certain cosmological puzzles by positing that the universe passes through innite cycles (aeons), with conformal rescaling connecting the end of one aeon to the be ginning of the next. This paper examines the conceptual foundations of CCC, focusing on the distinction between conformal continuity (mathematical smoothness of the metric under rescaling) and physical continuity (preservation of causal and dynamical structure). The analysis identi es a category error at the heart of CCC: the con ation of loss of scale with cessation of physical process. When mass vanishes and scale becomes unde ned, CCC interprets this as an opportunity for geometric restart. However, conformal transformation is a coordinate operation that relabels existing structure; it does not generate new causal content. The smoothness of a mathematical map does not entail the continuity of the physical processes it represents. This paper does not propose an alternative cosmological model. Its aim is to clarify the conceptual boundaries of CCC's claims and to distinguish what the formalism computes from what it describes.