De Sitter Space (dS): A Model of Our Expanding Universe and Its Limitations

This article is an explanatory supplement to Article 8 of the main series, devoted to the concept of de Sitter space (dS) – the model of our acceleratingly expanding Universe. Using the intuitive example of an “inflating balloon”, it explains that dS has positive curvature and expands with acceleration (Λ > 0). A comparison is made with Minkowski flat space (Λ = 0, non‑expanding) and with Anti‑de Sitter space AdS (Λ < 0, static). The main difference between dS and AdS is the absence of a rigorously proven holographic correspondence. Attempts to construct dS/CFT face fundamental problems: the lack of a natural boundary at infinity and the non‑unitarity of the resulting theories. This means that all the beautiful results of AdS/CFT cannot be directly applied to our Universe — transferring them to real astrophysical collapsars is only a hypothetical extrapolation. The article clarifies the limitations that must be taken into account when using the holographic principle in cosmology and black hole (collapsar) physics. It notes that direct application of AdS/CFT to the expanding Universe is impossible, and discusses possible paths forward: developing dS/CFT, approximate methods, or alternative approaches to quantum gravity in dS. The article is addressed to readers encountering the concepts of AdS and dS for the first time and is recommended as a supplement to Article 8 of the main series.