For many years, I have been fascinated by the lingering puzzles surrounding cosmic acceleration—particularly the question of why the expansion of the universe appears to accelerate rather than decelerate.
While reflecting on this question, an intriguing thought experiment came to mind: What if the universe could be visualized as a static, spherically symmetric spacetime with a sparse center and an increasingly dense periphery, reminiscent of M. C. Escher’s Circle Limit series? In my own notes, I have tentatively called this the "Escher Model."
Within this conceptual framework, redshift could be interpreted as arising from gravitational potential gradients rather than from physical spatial expansion. This might offer an alternative, exploratory perspective on cosmic acceleration that does not necessarily rely on dark energy, as well as an alternative context for the cosmic microwave background.
In such a geometry, an internal observer measures this universe as an infinite and boundary-free space, whereas an outside observer would see it as a bounded finite sphere. However, strictly speaking, we can explore the physics of the interior, but the "outside" remains inherently unobservable for an internal observer. As Ludwig Wittgenstein famously wrote, "Whereof one cannot speak, thereof one must be silent". We have neither metrics, physical constants, nor clocks to meaningfully characterize an external realm.
I wish to emphasize that I do not claim the standard expanding universe paradigm is wrong, nor do I claim that this Escher-inspired model is a proven alternative. I deeply respect the achievements of modern cosmology and remain open to many frameworks, including the multiverse of quantum cosmology.
My sincere intention is to share this thought experiment as an open invitation for constructive discussion. I wonder whether exploring the interplay between conventional expansion theories and this geometric perspective could help us better understand future observational data. My thoughts continue to evolve every day, and I would be truly grateful to learn from your insights and explore these fundamental questions together.
10.5281/zenodo.21868831
https://t.co/TvP5FfGGSm